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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 6 and 7. 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 6 and 7. 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 6 and 7?</h2>
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<h2>What is the LCM of 6 and 7?</h2>
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<h2>How to find the LCM of 6 and 7?</h2>
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<h2>How to find the LCM of 6 and 7?</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 6 and 7 using the Listing Multiples Method</h3>
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<h3>LCM of 6 and 7 using the Listing Multiples Method</h3>
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<p>The LCM of 6 and 7 can be found using the following steps:</p>
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<p>The LCM of 6 and 7 can be found using the following steps:</p>
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<p><strong>Step 1:</strong>Write down the multiples of each number</p>
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<p><strong>Step 1:</strong>Write down the multiples of each number</p>
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<p>Multiples of 6 = 6,12,…42,…</p>
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<p>Multiples of 6 = 6,12,…42,…</p>
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<p>Multiples of 7 = 7,14,…42,…</p>
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<p>Multiples of 7 = 7,14,…42,…</p>
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<p><strong>Step 2:</strong>Ascertain the smallest<a>common multiple</a>from the listed multiples</p>
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<p><strong>Step 2:</strong>Ascertain the smallest<a>common multiple</a>from the listed multiples</p>
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<p> The smallest common multiple is 42</p>
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<p> The smallest common multiple is 42</p>
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<p>Thus, LCM(6, 7) = 42. </p>
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<p>Thus, LCM(6, 7) = 42. </p>
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<h3>LCM of 6 and 7 using the Prime Factorization Method</h3>
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<h3>LCM of 6 and 7 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>Step 1:</strong>Find the prime factors of the numbers:</p>
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<p><strong>Step 1:</strong>Find the prime factors of the numbers:</p>
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<p>Prime factorization of 6 = 2×3</p>
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<p>Prime factorization of 6 = 2×3</p>
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<p> Prime factorization of 7 = 7</p>
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<p> Prime factorization of 7 = 7</p>
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<p><strong>Step 2:</strong>Take the highest powers of each prime factor:</p>
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<p><strong>Step 2:</strong>Take the highest powers of each prime factor:</p>
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<p>Highest power of prime factors= 2,3</p>
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<p>Highest power of prime factors= 2,3</p>
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<p>Highest power of prime factor = 7</p>
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<p>Highest power of prime factor = 7</p>
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<p><strong>Step 3:</strong> Multiply the highest powers to get the LCM:</p>
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<p><strong>Step 3:</strong> Multiply the highest powers to get the LCM:</p>
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<p>LCM(6, 7) = 2 ×3 × 7= 42</p>
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<p>LCM(6, 7) = 2 ×3 × 7= 42</p>
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<h3>LCM of 6 and 7 using the Division Method</h3>
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<h3>LCM of 6 and 7 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>Step 1: Write the numbers, divide by common prime factors and multiply the divisors.</p>
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<p>Step 1: Write the numbers, divide by common prime factors and multiply the divisors.</p>
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<p><strong>Step 2:</strong> A prime<a>integer</a>that is evenly divisible into at least one of the provided numbers should be used to divide the row of numbers. Continue dividing the numbers until the last row of the results is ‘1’ and bring down the numbers not divisible by the previously chosen<a>prime number</a>.</p>
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<p><strong>Step 2:</strong> A prime<a>integer</a>that is evenly divisible into at least one of the provided numbers should be used to divide the row of numbers. Continue dividing the numbers until the last row of the results is ‘1’ and bring down the numbers not divisible by the previously chosen<a>prime number</a>.</p>
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<p><strong>Step 3:</strong> 2× 3 × 7= 42</p>
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<p><strong>Step 3:</strong> 2× 3 × 7= 42</p>
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<h2>Common Mistakes and how to avoid them in LCM of 6 and 7</h2>
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<h2>Common Mistakes and how to avoid them in LCM of 6 and 7</h2>
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<p>Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 6 and 7, 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 6 and 7, 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>What is the least perfect square divisible by 6 and 7?</p>
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<p>What is the least perfect square divisible by 6 and 7?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>Follow the below steps to find the least perfect square that is divisible by the numbers 6 and 7; </p>
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<p>Follow the below steps to find the least perfect square that is divisible by the numbers 6 and 7; </p>
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<p><strong>Step 1</strong>- Prime factorize the numbers </p>
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<p><strong>Step 1</strong>- Prime factorize the numbers </p>
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<p>6 = 2×3</p>
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<p>6 = 2×3</p>
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<p>7 = 7</p>
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<p>7 = 7</p>
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<p><strong>Step 2 </strong>- Find the LCM </p>
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<p><strong>Step 2 </strong>- Find the LCM </p>
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<p>LCM(6,7) = 2×3×7 = 42</p>
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<p>LCM(6,7) = 2×3×7 = 42</p>
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<p><strong>Step 3</strong>- Adjust the numbers for a perfect square, to do so to make all the exponents even. Multiply the numbers</p>
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<p><strong>Step 3</strong>- Adjust the numbers for a perfect square, to do so to make all the exponents even. Multiply the numbers</p>
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<p>21×31×71, which will give;</p>
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<p>21×31×71, which will give;</p>
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<p> 42×42 = 22×32×72 = 1764 </p>
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<p> 42×42 = 22×32×72 = 1764 </p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>The least perfect square divisible by both the numbers is 1764. </p>
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<p>The least perfect square divisible by both the numbers is 1764. </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>Elaborate on the relationship between HCF and LCM of 6 and 7.</p>
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<p>Elaborate on the relationship between HCF and LCM of 6 and 7.</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 relationship between HCF and LCM can be verified using this formula; HCF(a,b)×LCM(a,b) = a×b</p>
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<p>The relationship between HCF and LCM can be verified using this formula; HCF(a,b)×LCM(a,b) = a×b</p>
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<p>HCF of 6,7 = 1 (6,7 are relatively prime numbers) </p>
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<p>HCF of 6,7 = 1 (6,7 are relatively prime numbers) </p>
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<p>LCM of 6,7 = 42</p>
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<p>LCM of 6,7 = 42</p>
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<p>Now apply the formula, </p>
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<p>Now apply the formula, </p>
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<p>HCF(a,b)×LCM(a,b) = a×b</p>
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<p>HCF(a,b)×LCM(a,b) = a×b</p>
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<p>HCF(6,7)×LCM(6,7) = 6×7</p>
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<p>HCF(6,7)×LCM(6,7) = 6×7</p>
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<p>1×42 = 42 </p>
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<p>1×42 = 42 </p>
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<p>42 = 42</p>
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<p>42 = 42</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p> The above explains the relationship between the HCF and the LCM of 6 and 7. The given formula works to verify the relationship between the HCF and LCM for any given pair of numbers. </p>
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<p> The above explains the relationship between the HCF and the LCM of 6 and 7. The given formula works to verify the relationship between the HCF and LCM for any given pair of numbers. </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>Find the LCM of 6 and 7 using a Venn diagram.</p>
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<p>Find the LCM of 6 and 7 using a Venn diagram.</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>List the factors of the numbers;</p>
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<p>List the factors of the numbers;</p>
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<p>- 6 -> 2,3</p>
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<p>- 6 -> 2,3</p>
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<p>- 7 -> 7 </p>
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<p>- 7 -> 7 </p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p> The numbers have no common factors, therefore the numbers are listed in their own circles and are multiplied. The LCM (6,7) = 42. </p>
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<p> The numbers have no common factors, therefore the numbers are listed in their own circles and are multiplied. The LCM (6,7) = 42. </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>Elevator F stops on the first floor every 6 minutes and elevator Y stops every 7 minutes. If they both stop on the first floor now, when will they both stop at the same time next?</p>
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<p>Elevator F stops on the first floor every 6 minutes and elevator Y stops every 7 minutes. If they both stop on the first floor now, when will they both stop at the same time next?</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 6 and 7 is 42. </p>
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<p>The LCM of 6 and 7 is 42. </p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>The smallest common multiple between the numbers 6 and 7 is 42. So, we can say that in 42 minutes, elevators F and Y will stop at the same time on the first floor. </p>
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<p>The smallest common multiple between the numbers 6 and 7 is 42. So, we can say that in 42 minutes, elevators F and Y will stop at the same time on the first floor. </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 6 and 7</h2>
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<h2>FAQs on LCM of 6 and 7</h2>
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<h3>1.What do 6 and 7 have in common?</h3>
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<h3>1.What do 6 and 7 have in common?</h3>
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<p>6 and 7 share distinct prime factor<a>combinations</a>, the only common factor they share is 1. </p>
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<p>6 and 7 share distinct prime factor<a>combinations</a>, the only common factor they share is 1. </p>
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<p>Factors of 6: 1,2,3,6</p>
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<p>Factors of 6: 1,2,3,6</p>
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<p>Factors of 7: 1,7 </p>
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<p>Factors of 7: 1,7 </p>
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<h3>2.Is 42 a multiple of 6 and 7?</h3>
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<h3>2.Is 42 a multiple of 6 and 7?</h3>
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<p>Yes, 42 is a multiple of both 6 and 7. 6 times 7 and vice versa is 42. </p>
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<p>Yes, 42 is a multiple of both 6 and 7. 6 times 7 and vice versa is 42. </p>
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<h3>3.Is 69 a multiple of 6?</h3>
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<h3>3.Is 69 a multiple of 6?</h3>
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<p>No, 69 is not a multiple of 6. When divided, it leaves behind a<a>remainder</a>of 3.</p>
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<p>No, 69 is not a multiple of 6. When divided, it leaves behind a<a>remainder</a>of 3.</p>
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<h3>4.Is 42 the LCM of 6 and 7?</h3>
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<h3>4.Is 42 the LCM of 6 and 7?</h3>
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<p>Yes, the LCM of 6 and 7 is 42. The numbers have no common factors, and the least common multiple they share is 42. </p>
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<p>Yes, the LCM of 6 and 7 is 42. The numbers have no common factors, and the least common multiple they share is 42. </p>
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<h3>5.What is the LCM of 6,7 and 9?</h3>
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<h3>5.What is the LCM of 6,7 and 9?</h3>
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<p><strong>Step 1:</strong>Find the prime factors of the numbers:</p>
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<p><strong>Step 1:</strong>Find the prime factors of the numbers:</p>
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<p>Prime factorization of 6 = 2×3</p>
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<p>Prime factorization of 6 = 2×3</p>
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<p>Prime factorization of 7 = 7</p>
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<p>Prime factorization of 7 = 7</p>
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<p>Prime factorization of 9 = 3×3</p>
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<p>Prime factorization of 9 = 3×3</p>
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<p><strong>Step 2:</strong>Take the highest powers of each prime factor:</p>
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<p><strong>Step 2:</strong>Take the highest powers of each prime factor:</p>
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<p>Highest power of 6 = 21,31</p>
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<p>Highest power of 6 = 21,31</p>
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<p>Highest power of 7 = 7</p>
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<p>Highest power of 7 = 7</p>
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<p>Highest power of 9 = 32</p>
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<p>Highest power of 9 = 32</p>
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<p><strong>Step 3:</strong>Multiply the highest powers to get the LCM:</p>
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<p><strong>Step 3:</strong>Multiply the highest powers to get the LCM:</p>
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<p>LCM(6, 7,9) = 2 ×32× 7= 126 </p>
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<p>LCM(6, 7,9) = 2 ×32× 7= 126 </p>
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<h2>Important glossaries for the LCM of 6 and 7</h2>
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<h2>Important glossaries for the LCM of 6 and 7</h2>
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<ul><li><strong>Prime Factor:</strong>A natural number (other than 1) whose factors are only one and itself.</li>
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<ul><li><strong>Prime Factor:</strong>A natural number (other than 1) whose factors are only 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>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><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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