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2026-01-01
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<p>Last updated on<strong>August 5, 2025</strong></p>
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<p>Last updated on<strong>August 5, 2025</strong></p>
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<p>The Least common multiple (LCM) is the smallest number that is divisible by the numbers 10 and 12. The LCM can be found using the listing multiples method, the prime factorization and/or division methods. LCM helps to solve problems with fractions and scenarios like scheduling or aligning repeating cycle of events.</p>
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<p>The Least common multiple (LCM) is the smallest number that is divisible by the numbers 10 and 12. The LCM can be found using the listing multiples method, the prime factorization and/or division methods. LCM helps to solve problems with fractions and scenarios like scheduling or aligning repeating cycle of events.</p>
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<h2>What is the LCM of 10 and 12?</h2>
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<h2>What is the LCM of 10 and 12?</h2>
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<h2>How to find the LCM of 10 and 12?</h2>
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<h2>How to find the LCM of 10 and 12?</h2>
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<p>There are various methods to find the LCM, Listing method,<a>prime factorization</a>method and<a>division</a>method are explained below;</p>
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<p>There are various methods to find the LCM, Listing method,<a>prime factorization</a>method and<a>division</a>method are explained below;</p>
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<h3>LCM of 10 and 12 using the Listing Multiples Method</h3>
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<h3>LCM of 10 and 12 using the Listing Multiples Method</h3>
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<p>The LCM of 10 and 12 can be found using the following steps:</p>
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<p>The LCM of 10 and 12 can be found using the following steps:</p>
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<p><strong>Steps:</strong></p>
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<p><strong>Steps:</strong></p>
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<p>1. Write down the multiples of each number</p>
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<p>1. Write down the multiples of each number</p>
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<p> - Multiples of 10 = 10, 20, 30, 40, 50, 60, …</p>
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<p> - Multiples of 10 = 10, 20, 30, 40, 50, 60, …</p>
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<p> - Multiples of 12 = 12, 24, 36, 48, 60, …</p>
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<p> - Multiples of 12 = 12, 24, 36, 48, 60, …</p>
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<p>2. Ascertain the smallest multiple from the listed multiples</p>
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<p>2. Ascertain the smallest multiple from the listed multiples</p>
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<p> - The smallest<a>common multiple</a>is 60.</p>
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<p> - The smallest<a>common multiple</a>is 60.</p>
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<p>Thus, LCM(10, 12) = 60.</p>
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<p>Thus, LCM(10, 12) = 60.</p>
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<h3>LCM of 10 and 12 using the Prime Factorization Method</h3>
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<h3>LCM of 10 and 12 using the Prime Factorization Method</h3>
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<p>The prime<a>factors</a>of each number are written, and then the highest<a>power</a>of the prime factors is multiplied to get the LCM.</p>
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<p>The prime<a>factors</a>of each number are written, and then the highest<a>power</a>of the prime factors is multiplied to get the LCM.</p>
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<p><strong>Steps:</strong></p>
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<p><strong>Steps:</strong></p>
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<p>1. Find the prime factors of the numbers:</p>
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<p>1. Find the prime factors of the numbers:</p>
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<p> - Prime factorization of 10 = 2 × 5</p>
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<p> - Prime factorization of 10 = 2 × 5</p>
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<p> - Prime factorization of 12 = 2 × 2 × 3</p>
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<p> - Prime factorization of 12 = 2 × 2 × 3</p>
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<p>2. Take the highest powers of each prime factor:</p>
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<p>2. Take the highest powers of each prime factor:</p>
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<p> - Highest power of 2 = 2²</p>
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<p> - Highest power of 2 = 2²</p>
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<p> - Highest power of 3 = 3</p>
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<p> - Highest power of 3 = 3</p>
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<p> - Highest power of 5 = 5</p>
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<p> - Highest power of 5 = 5</p>
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<ol><li><strong> Multiply the highest powers to get the LCM:</strong></li>
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<ol><li><strong> Multiply the highest powers to get the LCM:</strong></li>
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</ol><p> LCM(10, 12) = 2² × 3 × 5 = 60</p>
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</ol><p> LCM(10, 12) = 2² × 3 × 5 = 60</p>
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<h3>LCM of 10 and 12 using the Division Method</h3>
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<h3>LCM of 10 and 12 using the Division Method</h3>
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<p>This method involves dividing both numbers by their common prime factors until no further division is possible, then multiplying the divisors to find the LCM.</p>
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<p>This method involves dividing both numbers by their common prime factors until no further division is possible, then multiplying the divisors to find the LCM.</p>
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<p><strong>Steps:</strong></p>
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<p><strong>Steps:</strong></p>
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<p>1. Write the numbers:</p>
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<p>1. Write the numbers:</p>
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<p>2. Divide by common prime factors and multiply the divisors: </p>
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<p>2. Divide by common prime factors and multiply the divisors: </p>
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<p> - 2 × 2 × 3 × 5 = 60</p>
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<p> - 2 × 2 × 3 × 5 = 60</p>
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<p>Thus, LCM(10, 12) = 60.</p>
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<p>Thus, LCM(10, 12) = 60.</p>
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<h2>Common Mistakes and how to avoid them while finding the LCM of 10 and 12</h2>
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<h2>Common Mistakes and how to avoid them while finding the LCM of 10 and 12</h2>
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<p>Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 10 and 12, make a note while practicing.</p>
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<p>Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 10 and 12, make a note while practicing.</p>
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<h3>Problem 1</h3>
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<h3>Problem 1</h3>
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<p>Bus A and bus B, run every 10 and 12 days, both leave the station today. When will they next leave the station on the same day again?</p>
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<p>Bus A and bus B, run every 10 and 12 days, both leave the station today. When will they next leave the station on the same day again?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The LCM of 10 and 12 is 60</p>
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<p>The LCM of 10 and 12 is 60</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>The buses will leave together next in 60 days. 60 is the LCM of 10 and 12, expressing the smallest time interval between the digits.</p>
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<p>The buses will leave together next in 60 days. 60 is the LCM of 10 and 12, expressing the smallest time interval between the digits.</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 2</h3>
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<h3>Problem 2</h3>
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<p>In a neighborhood park, the fountain show is turned on every 10 minutes, and the light show every 12 minutes. If both the shows are turned on at the same time, when will they next be turned on together again?</p>
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<p>In a neighborhood park, the fountain show is turned on every 10 minutes, and the light show every 12 minutes. If both the shows are turned on at the same time, when will they next be turned on together again?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The LCM of 10 and 12 is 60.</p>
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<p>The LCM of 10 and 12 is 60.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Both the shows will turn on at the same time in 60 minutes,60 is the LCM of 10 and 12, expressing the smallest time interval between the digits.</p>
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<p>Both the shows will turn on at the same time in 60 minutes,60 is the LCM of 10 and 12, expressing the smallest time interval between the digits.</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 3</h3>
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<h3>Problem 3</h3>
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<p>The sprinkler watering system waters every 10 days and the drip watering system waters every 12 days. On which day do they have to be turned on together?</p>
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<p>The sprinkler watering system waters every 10 days and the drip watering system waters every 12 days. On which day do they have to be turned on together?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The LCM of 10 and 12 is 60</p>
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<p>The LCM of 10 and 12 is 60</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Both the watering systems have to be turned on together in 60 days. 60 is the LCM of 10 and 12, expressing the smallest time interval between the digits.</p>
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<p>Both the watering systems have to be turned on together in 60 days. 60 is the LCM of 10 and 12, expressing the smallest time interval between the digits.</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 4</h3>
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<h3>Problem 4</h3>
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<p>A car mechanic services a red car every 10 days and a blue car every 12 days. If the cars are serviced today, when will they be serviced next together?</p>
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<p>A car mechanic services a red car every 10 days and a blue car every 12 days. If the cars are serviced today, when will they be serviced next together?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The LCM of 10 and 12 is 60.</p>
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<p>The LCM of 10 and 12 is 60.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Both cars will be serviced again in 60 days.60 is the LCM of 10 and 12, expressing the smallest time interval between the digits.</p>
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<p>Both cars will be serviced again in 60 days.60 is the LCM of 10 and 12, expressing the smallest time interval between the digits.</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h2>FAQs on LCM of 10 and 12</h2>
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<h2>FAQs on LCM of 10 and 12</h2>
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<h3>1.How do you find the LCM of 10 and 12 using a Venn diagram?</h3>
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<h3>1.How do you find the LCM of 10 and 12 using a Venn diagram?</h3>
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<p>Follow the below steps to ascertain the LCM of 10 and 12 using a Venn diagram;</p>
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<p>Follow the below steps to ascertain the LCM of 10 and 12 using a Venn diagram;</p>
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<p>1. List the prime factors of the digits </p>
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<p>1. List the prime factors of the digits </p>
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<p> - Prime factorization of 10 = 2 × 5</p>
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<p> - Prime factorization of 10 = 2 × 5</p>
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<p> - Prime factorization of 12 = 2 × 2 × 3</p>
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<p> - Prime factorization of 12 = 2 × 2 × 3</p>
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<p>2. Place the factors in the diagram</p>
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<p>2. Place the factors in the diagram</p>
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<ul><li>2 is a<a>common factor</a>, place it in the overlapping section. </li>
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<ul><li>2 is a<a>common factor</a>, place it in the overlapping section. </li>
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<li>5,2,3 are unique factors ascertained after the common factor for 10 and 12. Place them in their own section. </li>
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<li>5,2,3 are unique factors ascertained after the common factor for 10 and 12. Place them in their own section. </li>
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<li>Now, multiply both the common and the unique factors - 2 × 2 × 3×5 = 60</li>
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<li>Now, multiply both the common and the unique factors - 2 × 2 × 3×5 = 60</li>
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<li>The LCM (10,12) = 60. </li>
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<li>The LCM (10,12) = 60. </li>
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</ul><h3>2.What is the LCM formula using the HCF? Explain for the numbers 10 and 12.</h3>
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</ul><h3>2.What is the LCM formula using the HCF? Explain for the numbers 10 and 12.</h3>
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<p>The LCM can be found using the<a>formula</a>, and as explained with the example given below. </p>
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<p>The LCM can be found using the<a>formula</a>, and as explained with the example given below. </p>
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<p>LCM (a, b)= a×b/HCF(a, b)</p>
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<p>LCM (a, b)= a×b/HCF(a, b)</p>
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<p>For 6 and 10, HCF(10,12)= 2</p>
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<p>For 6 and 10, HCF(10,12)= 2</p>
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<p>So, LCM(10,12)=10×12/2 = 60</p>
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<p>So, LCM(10,12)=10×12/2 = 60</p>
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<h3>3.How do you derive the LCM of two decimal numbers? Explain using 10.0 and 12.0.</h3>
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<h3>3.How do you derive the LCM of two decimal numbers? Explain using 10.0 and 12.0.</h3>
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<p>To derive the LCM of two<a>decimal numbers</a>, follow the below steps;</p>
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<p>To derive the LCM of two<a>decimal numbers</a>, follow the below steps;</p>
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<p>First, convert the given decimals to<a>whole numbers</a>. In the given case, 10.0 and 12.0 are already whole. However, if there is a case where the decimal is, say, 4.5, multiply it by 10 to convert them to a whole number, which will be 45. After converting them into whole numbers, ascertain the LCM of the digits using any of the methods, i.e., the listing multiples method, the division method or the prime factorization method. The LCM (10,12)= 60</p>
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<p>First, convert the given decimals to<a>whole numbers</a>. In the given case, 10.0 and 12.0 are already whole. However, if there is a case where the decimal is, say, 4.5, multiply it by 10 to convert them to a whole number, which will be 45. After converting them into whole numbers, ascertain the LCM of the digits using any of the methods, i.e., the listing multiples method, the division method or the prime factorization method. The LCM (10,12)= 60</p>
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<h3>4.How do you find the LCM of algebraic expressions?</h3>
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<h3>4.How do you find the LCM of algebraic expressions?</h3>
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<p>For<a>algebraic expressions</a>, find the LCM by factoring each expression and then choosing the highest power of each<a>variable</a>. </p>
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<p>For<a>algebraic expressions</a>, find the LCM by factoring each expression and then choosing the highest power of each<a>variable</a>. </p>
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<p>For example, Find the LCM of<em>x2y</em>and<em>xy3</em></p>
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<p>For example, Find the LCM of<em>x2y</em>and<em>xy3</em></p>
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<ul><li>Factor each<a>term</a>as follows</li>
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<ul><li>Factor each<a>term</a>as follows</li>
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</ul><p><em>x</em><em>2</em><em>y</em>=<em>x</em><em>2</em><em> </em>×<em>y</em>----> highest power = <em>x</em><em>2 </em></p>
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</ul><p><em>x</em><em>2</em><em>y</em>=<em>x</em><em>2</em><em> </em>×<em>y</em>----> highest power = <em>x</em><em>2 </em></p>
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<p><em>xy</em><em>3</em>= x ×<em> y</em><em>3</em><em> </em>----> highest power =<em> y</em><em>3 </em></p>
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<p><em>xy</em><em>3</em>= x ×<em> y</em><em>3</em><em> </em>----> highest power =<em> y</em><em>3 </em></p>
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<p>Multiply the highest powers ----><em>x</em><em>2</em><em>y</em><em>3 </em></p>
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<p>Multiply the highest powers ----><em>x</em><em>2</em><em>y</em><em>3 </em></p>
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<p><em> </em>LCM(<em>x</em><em>2</em><em>y</em>,<em>xy</em><em>3</em><em>) = x</em><em>2</em><em>y3</em></p>
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<p><em> </em>LCM(<em>x</em><em>2</em><em>y</em>,<em>xy</em><em>3</em><em>) = x</em><em>2</em><em>y3</em></p>
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<h2>Important glossaries for LCM of 10 and 12</h2>
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<h2>Important glossaries for LCM of 10 and 12</h2>
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<ul><li><strong>Multiple:</strong>A number and any integer multiplied. </li>
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<ul><li><strong>Multiple:</strong>A number and any integer multiplied. </li>
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</ul><ul><li><strong>Prime Factor:</strong>A natural number (other than 1) that has factors that are one and itself.</li>
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</ul><ul><li><strong>Prime Factor:</strong>A natural number (other than 1) that has factors that are one and itself.</li>
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</ul><ul><li><strong>Prime Factorization:</strong>The process of breaking down a number into its prime factors is called Prime Factorization. </li>
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</ul><ul><li><strong>Prime Factorization:</strong>The process of breaking down a number into its prime factors is called Prime Factorization. </li>
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</ul><ul><li><strong>Co-prime numbers:</strong>When the only positive integer that is a divisor of them both is 1, a number is co-prime. </li>
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</ul><ul><li><strong>Co-prime numbers:</strong>When the only positive integer that is a divisor of them both is 1, a number is co-prime. </li>
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</ul><ul><li><strong>Relatively Prime Numbers:</strong>Numbers that have no common factors other than 1.</li>
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</ul><ul><li><strong>Relatively Prime Numbers:</strong>Numbers that have no common factors other than 1.</li>
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</ul><ul><li><strong>Fraction:</strong>A representation of a part of a whole.</li>
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</ul><ul><li><strong>Fraction:</strong>A representation of a part of a whole.</li>
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</ul><p>What Are Numbers? 🔢 | Fun Explanation with 🎯 Real-Life Examples for Kids | ✨BrightCHAMPS Math</p>
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</ul><p>What Are Numbers? 🔢 | Fun Explanation with 🎯 Real-Life Examples for Kids | ✨BrightCHAMPS Math</p>
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<p>▶</p>
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<h2>Hiralee Lalitkumar Makwana</h2>
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<h2>Hiralee Lalitkumar Makwana</h2>
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<h3>About the Author</h3>
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<h3>About the Author</h3>
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<p>Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.</p>
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<p>Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.</p>
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<h3>Fun Fact</h3>
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<h3>Fun Fact</h3>
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<p>: She loves to read number jokes and games.</p>
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<p>: She loves to read number jokes and games.</p>