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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 7 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 7 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 7 and 12?</h2>
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<h2>What is the LCM of 7 and 12?</h2>
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<h2>How to Find the LCM of 7 and 12?</h2>
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<h2>How to Find the LCM of 7 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 7 and 12 using the Listing Multiples Method</h3>
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<h3>LCM of 7 and 12 using the Listing Multiples Method</h3>
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<p>The LCM of 7 and 12 can be calculated using the following steps:</p>
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<p>The LCM of 7 and 12 can be calculated 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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<ol><li>Write down the multiples of each number</li>
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<ol><li>Write down the multiples of each number</li>
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</ol><p> - Multiples of 7 = 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, …</p>
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</ol><p> - Multiples of 7 = 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, …</p>
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<p> - Multiples of 12 = 12, 24, 36, 48, 60, 72, 84, …</p>
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<p> - Multiples of 12 = 12, 24, 36, 48, 60, 72, 84, …</p>
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<ol><li>Ascertain the smallest multiple from the listed multiples:</li>
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<ol><li>Ascertain the smallest multiple from the listed multiples:</li>
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</ol><p> - The smallest<a>common multiple</a>is 84.</p>
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</ol><p> - The smallest<a>common multiple</a>is 84.</p>
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<p>Thus, LCM(7, 12) = 84</p>
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<p>Thus, LCM(7, 12) = 84</p>
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<h3>LCM of 7 and 12 using the Prime Factorization Method</h3>
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<h3>LCM of 7 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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<ol><li> Prime factorization of 7 = 7 (since 7 is prime)</li>
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<ol><li> Prime factorization of 7 = 7 (since 7 is prime)</li>
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<li>Prime factorization of 12 = 2 × 2 × 3 </li>
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<li>Prime factorization of 12 = 2 × 2 × 3 </li>
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<li>Take the highest powers of each prime factor and multiply the highest powers to get the LCM:</li>
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<li>Take the highest powers of each prime factor and multiply the highest powers to get the LCM:</li>
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</ol><p>- LCM(7, 12) = 2² × 3 × 7 = 84</p>
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</ol><p>- LCM(7, 12) = 2² × 3 × 7 = 84</p>
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<h3>LCM of 7 and 12 using the Division Method</h3>
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<h3>LCM of 7 and 12 using the Division Method</h3>
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<p>This method involves dividing both numbers by their common prime factors and multiplying the divisors to find the LCM.</p>
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<p>This method involves dividing both numbers by their common prime factors and 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>- Write the numbers. Divide by common prime factors and multiply the divisors. </p>
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<p>- Write the numbers. Divide by common prime factors and multiply the divisors. </p>
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<p> - 2 × 2 × 3 × 7 = 84</p>
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<p> - 2 × 2 × 3 × 7 = 84</p>
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<p>Thus, LCM(7, 12) = 84</p>
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<p>Thus, LCM(7, 12) = 84</p>
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<h2>Common Mistakes and how to avoid them while finding the LCM of 7 and 12</h2>
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<h2>Common Mistakes and how to avoid them while finding the LCM of 7 and 12</h2>
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<p>Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 7 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 7 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>A movie theater alternates between a crime film and a children’s film. The crime film is shown every 7 days and the children’s film is shown every 12 days. In how many days will they both be screened together?</p>
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<p>A movie theater alternates between a crime film and a children’s film. The crime film is shown every 7 days and the children’s film is shown every 12 days. In how many days will they both be screened 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 7 and 12 is 84. </p>
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<p>The LCM of 7 and 12 is 84. </p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Both films will be shown on the same day again in 84 days. The LCM of 7 and 12 is 84, which is the smallest common time interval between the digits.</p>
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<p>Both films will be shown on the same day again in 84 days. The LCM of 7 and 12 is 84, which is the smallest common 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>An HP Printer prints a batch every 7 minutes and a Canon printer prints a batch every 12 minutes. If the machines start at 10:00 AM, when will they print out a batch at the same time?</p>
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<p>An HP Printer prints a batch every 7 minutes and a Canon printer prints a batch every 12 minutes. If the machines start at 10:00 AM, when will they print out a batch at the same time?</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 7 and 12 is 84.</p>
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<p>The LCM of 7 and 12 is 84.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Both machines will print a batch together at 11:24AM. The LCM of 7 and 12 is 84, which is the smallest common time interval between the digits.</p>
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<p>Both machines will print a batch together at 11:24AM. The LCM of 7 and 12 is 84, which is the smallest common 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 7 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 7 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 7 and 12 is 84.</p>
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<p>The LCM of 7 and 12 is 84.</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 84 days. The LCM of 7 and 12 is 84, which is the smallest common time interval between the digits.</p>
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<p>Both the watering systems have to be turned on together in 84 days. The LCM of 7 and 12 is 84, which is the smallest common 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>An assembly is held every 7 days and a debate competition every 12 days. If both the events occur today, in how many days will they occur together again?</p>
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<p>An assembly is held every 7 days and a debate competition every 12 days. If both the events occur today, in how many days will they occur 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 7 and 12 is 84.</p>
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<p>The LCM of 7 and 12 is 84.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>The events will occur together again in 84 days. The LCM of 7 and 12 is 84, which is the smallest common time interval between the digits.</p>
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<p>The events will occur together again in 84 days. The LCM of 7 and 12 is 84, which is the smallest common 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 7 and 12</h2>
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<h2>FAQs on LCM of 7 and 12</h2>
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<h3>1.Why is the LCM of 7 and 12 not simply their product (7 × 12 = 84) ?</h3>
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<h3>1.Why is the LCM of 7 and 12 not simply their product (7 × 12 = 84) ?</h3>
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<p>Multiplying gives you the product of the numbers. LCM, however, is the smallest common multiple that can be ascertained following the methods mentioned above.</p>
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<p>Multiplying gives you the product of the numbers. LCM, however, is the smallest common multiple that can be ascertained following the methods mentioned above.</p>
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<h3>2.How do you find the LCM with different bases in an exponential equation ?</h3>
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<h3>2.How do you find the LCM with different bases in an exponential equation ?</h3>
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<p>You can find the LCM For<a>exponential equations</a>with different bases by following the below example,</p>
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<p>You can find the LCM For<a>exponential equations</a>with different bases by following the below example,</p>
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<ul><li>Find the LCM of 74<strong>×</strong>122 and 73<strong>×</strong>123</li>
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<ul><li>Find the LCM of 74<strong>×</strong>122 and 73<strong>×</strong>123</li>
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<li>Factorize the<a>terms</a>and find the highest power </li>
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<li>Factorize the<a>terms</a>and find the highest power </li>
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</ul><p>Highest power of 7 = 74</p>
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</ul><p>Highest power of 7 = 74</p>
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<p>Highest power of 12= 123</p>
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<p>Highest power of 12= 123</p>
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<p>LCM = 74<strong>×</strong>123</p>
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<p>LCM = 74<strong>×</strong>123</p>
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<h3>3.What is the relationship between the Greatest Common Divisor (GCD)/ Highest Common Factor (HCF) and LCM of 7 and 12?</h3>
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<h3>3.What is the relationship between the Greatest Common Divisor (GCD)/ Highest Common Factor (HCF) and LCM of 7 and 12?</h3>
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<ul><li>The relationship between GCD and LCM is expressed by the<a>formula</a>: </li>
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<ul><li>The relationship between GCD and LCM is expressed by the<a>formula</a>: </li>
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</ul><p> LCM(a,b)×HCF(a,b)=a×b</p>
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</ul><p> LCM(a,b)×HCF(a,b)=a×b</p>
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<p>Verifying this, </p>
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<p>Verifying this, </p>
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<p>LCM(7,12)×HCF(7,12)= 84×1</p>
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<p>LCM(7,12)×HCF(7,12)= 84×1</p>
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<p>-> 84=84</p>
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<p>-> 84=84</p>
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<p>This formula shows how the GCD/HCF and LCM complement each other.</p>
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<p>This formula shows how the GCD/HCF and LCM complement each other.</p>
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<h3>5.Find the LCM of 7 and 12 using the continuous division method.</h3>
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<h3>5.Find the LCM of 7 and 12 using the continuous division method.</h3>
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<h2>Important glossaries for the LCM of 7 and 12</h2>
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<h2>Important glossaries for the LCM of 7 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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<li><strong>Prime Factor:</strong>A natural number (other than 1) that has factors that are one and itself.</li>
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<li><strong>Prime Factor:</strong>A natural number (other than 1) that has factors that are one and itself.</li>
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<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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<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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<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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<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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<li><strong>Relatively Prime Numbers:</strong>Numbers that have no common factors other than 1.</li>
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<li><strong>Relatively Prime Numbers:</strong>Numbers that have no common factors other than 1.</li>
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<li><strong>Fraction:</strong>A representation of a part or a whole</li>
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<li><strong>Fraction:</strong>A representation of a part or 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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<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>