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2 <p>Last updated on<strong>August 5, 2025</strong></p>

3 <p>The Least common multiple (LCM) is the smallest number that is divisible by the numbers 2 and 6. LCM helps to solve problems with fractions and scenarios like scheduling or aligning repeating cycle of events.</p>

4 <h2>What is the LCM of 2 and 6?</h2>

5 <h2>How to find the LCM of 2 and 6 ?</h2>

6 <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>

7 <h3>LCM of 2 and 6 using the Listing multiples method</h3>

8 <p>To ascertain the LCM, list the multiples of the<a>integers</a>until a<a>common multiple</a>is found. </p>

9 <p><strong>Step 1:</strong> Writedown the multiples of each number: </p>

10 <p>Multiples of 2 = 2,4,6,8,10,12…</p>

11 <p>Multiples of 6 = 6,12,18… </p>

12 <p><strong>Step 2:</strong> Ascertain the smallest multiple from the listed multiples of 2 and 6. </p>

13 <p>The LCM (The Least common multiple) of 2 and 6 is 6. i.e.,6 is divisible by 2 and 6 with no reminder.</p>

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16 <h3>LCM of 2 and 6 using the Prime Factorization</h3>

15 <h3>LCM of 2 and 6 using the Prime Factorization</h3>

17 <p>This method involves finding the prime<a>factors</a>of each number and then multiplying the highest<a>power</a>of the prime factors to get the LCM.</p>

16 <p>This method involves finding the prime<a>factors</a>of each number and then multiplying the highest<a>power</a>of the prime factors to get the LCM.</p>

18 <p><strong>Step 1: </strong>Find the prime factors of the numbers:</p>

17 <p><strong>Step 1: </strong>Find the prime factors of the numbers:</p>

19 <p>Prime factorization of 2 = 2</p>

18 <p>Prime factorization of 2 = 2</p>

20 <p>Prime factorization of 6 = 2×3 </p>

19 <p>Prime factorization of 6 = 2×3 </p>

21 <p><strong>Step 2: </strong>Take the highest power of each prime factor:</p>

20 <p><strong>Step 2: </strong>Take the highest power of each prime factor:</p>

22 <p>2,3</p>

21 <p>2,3</p>

23 <p><strong>Step 3: </strong>Multiply the ascertained factors to get the LCM: </p>

22 <p><strong>Step 3: </strong>Multiply the ascertained factors to get the LCM: </p>

24 <p>LCM (2,6) = 2×3 = 6</p>

23 <p>LCM (2,6) = 2×3 = 6</p>

25 <h3>LCM of 2 and 6 using the Division Method</h3>

24 <h3>LCM of 2 and 6 using the Division Method</h3>

26 <p>The Division Method involves dividing the numbers by their prime factors and multiplying the divisors to get the LCM. <strong>Step 1: </strong>Write down the numbers in a row;</p>

25 <p>The Division Method involves dividing the numbers by their prime factors and multiplying the divisors to get the LCM. <strong>Step 1: </strong>Write down the numbers in a row;</p>

27 <p><strong>Step 2:</strong> Divide the row of numbers by a<a>prime number</a>that is evenly divisible into at least one of the given 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 prime number.</p>

26 <p><strong>Step 2:</strong> Divide the row of numbers by a<a>prime number</a>that is evenly divisible into at least one of the given 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 prime number.</p>

28 <p><strong>Step 3: </strong>The LCM of the numbers is the<a>product</a>of the prime numbers in the first column, i.e.,</p>

27 <p><strong>Step 3: </strong>The LCM of the numbers is the<a>product</a>of the prime numbers in the first column, i.e.,</p>

29 <p> 2×3= 6</p>

28 <p> 2×3= 6</p>

30 <p>LCM (2,6) = 6</p>

29 <p>LCM (2,6) = 6</p>

31 <h2>Common Mistakes and how to avoid them in LCM of 2 and 6</h2>

30 <h2>Common Mistakes and how to avoid them in LCM of 2 and 6</h2>

32 <p>Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 2 and 6 make a note while practicing. </p>

31 <p>Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 2 and 6 make a note while practicing. </p>

33 <h3>Problem 1</h3>

32 <h3>Problem 1</h3>

34 <p>Use LCM(a,b)=|a×b|/HCF(a,b) to find the LCM of 2 and 6.</p>

33 <p>Use LCM(a,b)=|a×b|/HCF(a,b) to find the LCM of 2 and 6.</p>

35 <p>Okay, lets begin</p>

34 <p>Okay, lets begin</p>

36 <p>Let us assume, a= 2 and b= 6.</p>

35 <p>Let us assume, a= 2 and b= 6.</p>

37 <p>Applying the formula; </p>

36 <p>Applying the formula; </p>

38 <p>LCM(a,b)=|a×b|/HCF(a,b)</p>

37 <p>LCM(a,b)=|a×b|/HCF(a,b)</p>

39 <p>HCF of 2,6: </p>

38 <p>HCF of 2,6: </p>

40 <p>Factors of 2 = 1,2</p>

39 <p>Factors of 2 = 1,2</p>

41 <p>Factors of 6 = 1,2,3,6</p>

40 <p>Factors of 6 = 1,2,3,6</p>

42 <p>HCF (2,6) = 2 </p>

41 <p>HCF (2,6) = 2 </p>

43 <p>LCM(2,6)=|2×6|/2</p>

42 <p>LCM(2,6)=|2×6|/2</p>

44 <p>12/2 = 6 </p>

43 <p>12/2 = 6 </p>

45 <h3>Explanation</h3>

44 <h3>Explanation</h3>

46 <p>The above is how we ascertain the LCM of the numbers using the formula</p>

45 <p>The above is how we ascertain the LCM of the numbers using the formula</p>

47 <p>Well explained 👍</p>

46 <p>Well explained 👍</p>

48 <h3>Problem 2</h3>

47 <h3>Problem 2</h3>

49 <p>Add the fractions 1/2 and 1/6.</p>

48 <p>Add the fractions 1/2 and 1/6.</p>

50 <p>Okay, lets begin</p>

49 <p>Okay, lets begin</p>

51 <p>First, we find the LCM of the denominators; </p>

50 <p>First, we find the LCM of the denominators; </p>

52 <p>Prime factorization of 2 = 2</p>

51 <p>Prime factorization of 2 = 2</p>

53 <p>Prime factorization of 6 = 2×3 </p>

52 <p>Prime factorization of 6 = 2×3 </p>

54 <p>LCM (2,6) = 6 </p>

53 <p>LCM (2,6) = 6 </p>

55 <p>Now, we equate the denominators;</p>

54 <p>Now, we equate the denominators;</p>

56 <p>1/2 ×3/3 = 3/6 </p>

55 <p>1/2 ×3/3 = 3/6 </p>

57 <p>The denominator of 1/6 is already the LCM, so we do not equate its denominator. </p>

56 <p>The denominator of 1/6 is already the LCM, so we do not equate its denominator. </p>

58 <p>We proceed to add the fractions; </p>

57 <p>We proceed to add the fractions; </p>

59 <p>3/6 + 1/6 = 4/6 → can be simplified to 2/3. </p>

58 <p>3/6 + 1/6 = 4/6 → can be simplified to 2/3. </p>

60 <h3>Explanation</h3>

59 <h3>Explanation</h3>

61 <p>The above is how we use LCM to find the sum of fractions. The same process can be applied to other arithmetic operations. </p>

60 <p>The above is how we use LCM to find the sum of fractions. The same process can be applied to other arithmetic operations. </p>

62 <p>Well explained 👍</p>

61 <p>Well explained 👍</p>

63 <h3>Problem 3</h3>

62 <h3>Problem 3</h3>

64 <p>LCM of a and b is 6 and the HCF of the same two numbers is 1. Find a and b.</p>

63 <p>LCM of a and b is 6 and the HCF of the same two numbers is 1. Find a and b.</p>

65 <p>Okay, lets begin</p>

64 <p>Okay, lets begin</p>

66 <p>Given; </p>

65 <p>Given; </p>

67 <p>LCM (a, b) = 6 </p>

66 <p>LCM (a, b) = 6 </p>

68 <p>HCF (a, b) = 1</p>

67 <p>HCF (a, b) = 1</p>

69 <p>a = 2, b =3</p>

68 <p>a = 2, b =3</p>

70 <h3>Explanation</h3>

69 <h3>Explanation</h3>

71 <p>For the LCM to be 6 and the HCF to be 1, the numbers have to be coprime, i.e., they have no common factors but 1. </p>

70 <p>For the LCM to be 6 and the HCF to be 1, the numbers have to be coprime, i.e., they have no common factors but 1. </p>

72 <p>LCM (3,2) = 6, HCF(2,3) =1 </p>

71 <p>LCM (3,2) = 6, HCF(2,3) =1 </p>

73 <p>Well explained 👍</p>

72 <p>Well explained 👍</p>

74 <h2>FAQ’s on the LCM of 2 and 6</h2>

73 <h2>FAQ’s on the LCM of 2 and 6</h2>

75 <h3>1.Is multiplying 2 and 6 the correct way to find the LCM?</h3>

74 <h3>1.Is multiplying 2 and 6 the correct way to find the LCM?</h3>

76 <p>No, multiplying gives you the product of the numbers, in this case,12. LCM, however, is the smallest common multiple that can be ascertained following the listing multiples method, prime factorization, or the division method. </p>

75 <p>No, multiplying gives you the product of the numbers, in this case,12. LCM, however, is the smallest common multiple that can be ascertained following the listing multiples method, prime factorization, or the division method. </p>

77 <h3>2.Why is the LCM of 2 and 6, not 6?</h3>

76 <h3>2.Why is the LCM of 2 and 6, not 6?</h3>

78 <p>6 is not a multiple of 2, so it can’t be the LCM. LCM has to be the smallest number that both 2 and 6 divide into, which is 12. </p>

77 <p>6 is not a multiple of 2, so it can’t be the LCM. LCM has to be the smallest number that both 2 and 6 divide into, which is 12. </p>

79 <h3>3.What is the LCM formula using the HCF?</h3>

78 <h3>3.What is the LCM formula using the HCF?</h3>

80 <p>The method below elaborates on how to derive the LCM using HCF (Highest common factor). An example is also attached to check the validity. </p>

79 <p>The method below elaborates on how to derive the LCM using HCF (Highest common factor). An example is also attached to check the validity. </p>

81 <p>LCM (a, b)= a×b/HCF(a, b)</p>

80 <p>LCM (a, b)= a×b/HCF(a, b)</p>

82 <p>For the given numbers 2 and 6, HCF(2,6)=2 </p>

81 <p>For the given numbers 2 and 6, HCF(2,6)=2 </p>

83 <p>So, LCM(2,6)=2×6/2 = 6</p>

82 <p>So, LCM(2,6)=2×6/2 = 6</p>

84 <p>By following the above, we can state that the LCM of numbers 2 and 6 can be found using their HCF, which is 2. </p>

83 <p>By following the above, we can state that the LCM of numbers 2 and 6 can be found using their HCF, which is 2. </p>

85 <h3>4.Is the LCM of 2 and 6 always a multiple of their HCF?</h3>

84 <h3>4.Is the LCM of 2 and 6 always a multiple of their HCF?</h3>

86 <p>The LCM is always a multiple of HCF. For the numbers 8 and 20, the HCF is 2, and 6 (the LCM) is a multiple of 2. </p>

85 <p>The LCM is always a multiple of HCF. For the numbers 8 and 20, the HCF is 2, and 6 (the LCM) is a multiple of 2. </p>

87 <h3>5.What is the LCM of 2,4,6 and 8 ?</h3>

86 <h3>5.What is the LCM of 2,4,6 and 8 ?</h3>

88 <p><strong>Step 1: </strong>Write the numbers</p>

87 <p><strong>Step 1: </strong>Write the numbers</p>

89 <p><strong>Step 2:</strong> Divide by common prime factors</p>

88 <p><strong>Step 2:</strong> Divide by common prime factors</p>

90 <p><strong>Step 3:</strong> Multiply the divisors: So, LCM(2,4,6,8) = 48 </p>

89 <p><strong>Step 3:</strong> Multiply the divisors: So, LCM(2,4,6,8) = 48 </p>

91 <h2>Important Glossaries for LCM of 2 and 6</h2>

90 <h2>Important Glossaries for LCM of 2 and 6</h2>

92 <ul><li><strong>Multiple:</strong>A number and any integer multiplied.</li>

91 <ul><li><strong>Multiple:</strong>A number and any integer multiplied.</li>

93 </ul><ul><li><strong>Prime Factor:</strong>A natural number (other than 1) that has factors that are one and itself.</li>

92 </ul><ul><li><strong>Prime Factor:</strong>A natural number (other than 1) that has factors that are one and itself.</li>

94 </ul><ul><li><strong>Prime Factorization:</strong>The process of breaking down a number into its prime factors is called Prime Factorization. </li>

93 </ul><ul><li><strong>Prime Factorization:</strong>The process of breaking down a number into its prime factors is called Prime Factorization. </li>

95 </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>

94 </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>

96 </ul><ul><li><strong>Relatively Prime Numbers: </strong>Numbers that have no common factors other than 1.</li>

95 </ul><ul><li><strong>Relatively Prime Numbers: </strong>Numbers that have no common factors other than 1.</li>

97 </ul><ul><li><strong>Fraction:</strong>A representation of a part of a whole.</li>

96 </ul><ul><li><strong>Fraction:</strong>A representation of a part of a whole.</li>

98 </ul><p>What Are Numbers? 🔢 | Fun Explanation with 🎯 Real-Life Examples for Kids | ✨BrightCHAMPS Math</p>

97 </ul><p>What Are Numbers? 🔢 | Fun Explanation with 🎯 Real-Life Examples for Kids | ✨BrightCHAMPS Math</p>

99 <p>▶</p>

98 <p>▶</p>

100 <h2>Hiralee Lalitkumar Makwana</h2>

99 <h2>Hiralee Lalitkumar Makwana</h2>

101 <h3>About the Author</h3>

100 <h3>About the Author</h3>

102 <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>

101 <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>

103 <h3>Fun Fact</h3>

102 <h3>Fun Fact</h3>

104 <p>: She loves to read number jokes and games.</p>

103 <p>: She loves to read number jokes and games.</p>