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1 - <p>328 Learners</p>

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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 3,6 and 8. The LCM can be found using the listing multiples method, the prime factorization and/or division methods. LCM is used to find out the rotation of wheel at regular intervals or mechanism of gears in cars.</p>

4 <h2>What is the LCM of 3,6 and 8?</h2>

5 <h2>How to find the LCM of 3,6 and 8?</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 3,6 and 8 using the Listing Multiples Method</h3>

8 <p>The LCM of 3,6 and 8 can be found using the following steps:</p>

9 <p><strong>Step 1:</strong>Write down the multiples of each number.</p>

10 <p>Multiples of 3 = 3,6,9,12,15,18,21,24,…</p>

11 <p>Multiples of 6 = 6,18,24,…</p>

12 <p>Multiples of 8 = 8,16,24,…</p>

13 <p><strong> Step 2:</strong>Ascertain the smallest multiple from the listed multiples</p>

14 <p>The smallest<a>common multiple</a>is 24 </p>

15 <p>Thus, LCM (3,6,8) = 24</p>

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18 <h3>LCM of 3,6 and 8 using the Prime Factorization Method</h3>

17 <h3>LCM of 3,6 and 8 using the Prime Factorization Method</h3>

19 <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>

18 <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>

20 <p>Steps:Find the prime factors of the numbers.</p>

19 <p>Steps:Find the prime factors of the numbers.</p>

21 <p>Prime factorization of 3 = 3</p>

20 <p>Prime factorization of 3 = 3</p>

22 <p>Prime factorization of 6 = 3×3</p>

21 <p>Prime factorization of 6 = 3×3</p>

23 <p>Prime factorization of 8 = 2×3×2</p>

22 <p>Prime factorization of 8 = 2×3×2</p>

24 <p>Take the highest powers of each prime factor, and multiply the highest powers to get the LCM</p>

23 <p>Take the highest powers of each prime factor, and multiply the highest powers to get the LCM</p>

25 <p>3×3×2×2 =24</p>

24 <p>3×3×2×2 =24</p>

26 <p>LCM(3,6, 8) = 24 </p>

25 <p>LCM(3,6, 8) = 24 </p>

27 <h3>LCM of 3,6 and 8 using the Division Method</h3>

26 <h3>LCM of 3,6 and 8 using the Division Method</h3>

28 <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>

27 <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>

29 <p><strong>Step 1:</strong>Write the numbers, divide by common prime factors and multiply the divisors.</p>

28 <p><strong>Step 1:</strong>Write the numbers, divide by common prime factors and multiply the divisors.</p>

30 <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. </p>

29 <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. </p>

31 <p><strong>Step 3:</strong>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>

30 <p><strong>Step 3:</strong>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>

32 <p><strong>Step 4:</strong>The LCM of the numbers is the<a>product</a>of the prime numbers in the first column, i.e., </p>

31 <p><strong>Step 4:</strong>The LCM of the numbers is the<a>product</a>of the prime numbers in the first column, i.e., </p>

33 <p>LCM (3,6,8) = 24</p>

32 <p>LCM (3,6,8) = 24</p>

34 <h2>Common Mistakes and how to avoid them while finding the LCM of 3,6 and 8</h2>

33 <h2>Common Mistakes and how to avoid them while finding the LCM of 3,6 and 8</h2>

35 <p>Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 3,6 and 8, make a note while practicing. </p>

34 <p>Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 3,6 and 8, make a note while practicing. </p>

36 <h3>Problem 1</h3>

35 <h3>Problem 1</h3>

37 <p>What number should be added to 50 that the resultant value is divisible by the LCM of 3,6 and 8?</p>

36 <p>What number should be added to 50 that the resultant value is divisible by the LCM of 3,6 and 8?</p>

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

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

39 <p>The LCM of 3,6 and 8 is 24. </p>

38 <p>The LCM of 3,6 and 8 is 24. </p>

40 <p>Let the number that is to be added be x , 50+x is divisible by 24. </p>

39 <p>Let the number that is to be added be x , 50+x is divisible by 24. </p>

41 <p>50/24 → 2 remainder </p>

40 <p>50/24 → 2 remainder </p>

42 <p>To make 50 divisible by 24, we need to add 24-2 = 22 </p>

41 <p>To make 50 divisible by 24, we need to add 24-2 = 22 </p>

43 <h3>Explanation</h3>

42 <h3>Explanation</h3>

44 <p>x = 22 and 50+22 = 72, which is divisible by the LCM of 3,6 and 8. </p>

43 <p>x = 22 and 50+22 = 72, which is divisible by the LCM of 3,6 and 8. </p>

45 <p>Well explained 👍</p>

44 <p>Well explained 👍</p>

46 <h3>Problem 2</h3>

45 <h3>Problem 2</h3>

47 <p>Verify LCM(a,b,c)×HCF(a,b,c) = a×b×c , where a=3, b=6 and c=8.</p>

46 <p>Verify LCM(a,b,c)×HCF(a,b,c) = a×b×c , where a=3, b=6 and c=8.</p>

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

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

49 <p>LCM of 3,6, 8;</p>

48 <p>LCM of 3,6, 8;</p>

50 <p>Prime factorization of 3 = 3</p>

49 <p>Prime factorization of 3 = 3</p>

51 <p>Prime factorization of 6 = 3×3</p>

50 <p>Prime factorization of 6 = 3×3</p>

52 <p>Prime factorization of 8 = 2×2×2</p>

51 <p>Prime factorization of 8 = 2×2×2</p>

53 <p>LCM(3,6,8) = 24 </p>

52 <p>LCM(3,6,8) = 24 </p>

54 <p>HCF of 3,6,8; </p>

53 <p>HCF of 3,6,8; </p>

55 <p>Factors of 3 = 1,3</p>

54 <p>Factors of 3 = 1,3</p>

56 <p>Factors of 6 = 1,3,6</p>

55 <p>Factors of 6 = 1,3,6</p>

57 <p>Factors of 8 = 1,2,4,8 </p>

56 <p>Factors of 8 = 1,2,4,8 </p>

58 <p>HCF (3,6,8) = 1</p>

57 <p>HCF (3,6,8) = 1</p>

59 <p>Verifying the above in the given formula; </p>

58 <p>Verifying the above in the given formula; </p>

60 <p>LCM(a,b,c)×HCF(a,b,c) = a×b×c</p>

59 <p>LCM(a,b,c)×HCF(a,b,c) = a×b×c</p>

61 <p>24×1 = 3×6×8</p>

60 <p>24×1 = 3×6×8</p>

62 <p>24 is not equal to 144.</p>

61 <p>24 is not equal to 144.</p>

63 <h3>Explanation</h3>

62 <h3>Explanation</h3>

64 <p>The given formula doesn’t stand true when trying to verify for more than two given digits.</p>

63 <p>The given formula doesn’t stand true when trying to verify for more than two given digits.</p>

65 <p>Well explained 👍</p>

64 <p>Well explained 👍</p>

66 <h3>Problem 3</h3>

65 <h3>Problem 3</h3>

67 <p>Solve for x. Let n= LCM (3,6,8)</p>

66 <p>Solve for x. Let n= LCM (3,6,8)</p>

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

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

69 <p>n/3x+n/6x+n/8x = 1 </p>

68 <p>n/3x+n/6x+n/8x = 1 </p>

70 <p>Simplify each term;</p>

69 <p>Simplify each term;</p>

71 <p>8/x+4/x+3/x = 1</p>

70 <p>8/x+4/x+3/x = 1</p>

72 <p>Combine the like terms</p>

71 <p>Combine the like terms</p>

73 <p>; 8+4+3/x = 1</p>

72 <p>; 8+4+3/x = 1</p>

74 <p>15/x = 1 </p>

73 <p>15/x = 1 </p>

75 <p>Solving for x; </p>

74 <p>Solving for x; </p>

76 <p>x = 15 </p>

75 <p>x = 15 </p>

77 <h3>Explanation</h3>

76 <h3>Explanation</h3>

78 <p>the above is how we solve for x in the given equation. </p>

77 <p>the above is how we solve for x in the given equation. </p>

79 <p>Well explained 👍</p>

78 <p>Well explained 👍</p>

80 <h2>FAQs on LCM of 3,6 and 8</h2>

79 <h2>FAQs on LCM of 3,6 and 8</h2>

81 <h3>1.What is the LCM of 2,3,6,8?</h3>

80 <h3>1.What is the LCM of 2,3,6,8?</h3>

82 <p>Prime factorization of 3 = 3</p>

81 <p>Prime factorization of 3 = 3</p>

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

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

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

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

85 <p>Prime factorization of 8 = 2×2×2</p>

84 <p>Prime factorization of 8 = 2×2×2</p>

86 <p>LCM (2,3,6,8) = 24 </p>

85 <p>LCM (2,3,6,8) = 24 </p>

87 <h3>2.What is the LCM of 1,3,6 and 8?</h3>

86 <h3>2.What is the LCM of 1,3,6 and 8?</h3>

88 <p>Prime factorization of 1 = 1</p>

87 <p>Prime factorization of 1 = 1</p>

89 <p>Prime factorization of 3 = 3</p>

88 <p>Prime factorization of 3 = 3</p>

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

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

91 <p>Prime factorization of 8 = 2×2×2</p>

90 <p>Prime factorization of 8 = 2×2×2</p>

92 <p>LCM (1,3,6,8) = 24 </p>

91 <p>LCM (1,3,6,8) = 24 </p>

93 <h3>3.Find the LCM of 3,6,8 and 12.</h3>

92 <h3>3.Find the LCM of 3,6,8 and 12.</h3>

94 <p>Prime factorization of 3 = 3</p>

93 <p>Prime factorization of 3 = 3</p>

95 <p>Prime factorization of 12 = 2×2×3</p>

94 <p>Prime factorization of 12 = 2×2×3</p>

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

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

97 <p>Prime factorization of 8 = 2×2×2</p>

96 <p>Prime factorization of 8 = 2×2×2</p>

98 <p>LCM (3,6,8,12)= 24 </p>

97 <p>LCM (3,6,8,12)= 24 </p>

99 <h3>4.List the multiples of 3,6 and 8.</h3>

98 <h3>4.List the multiples of 3,6 and 8.</h3>

100 <p> Multiples of 3 = 3,6,9,12,15,18,21,24,27,30,…</p>

99 <p> Multiples of 3 = 3,6,9,12,15,18,21,24,27,30,…</p>

101 <p> Multiples of 6 = 6,18,24,30,36,42,48,54,60,…</p>

100 <p> Multiples of 6 = 6,18,24,30,36,42,48,54,60,…</p>

102 <p> Multiples of 8 = 8,16,24,32,40,48,56,64,72,80,…</p>

101 <p> Multiples of 8 = 8,16,24,32,40,48,56,64,72,80,…</p>

103 <h3>5.What is the LCM of 3,5 and 6?</h3>

102 <h3>5.What is the LCM of 3,5 and 6?</h3>

104 <p>Prime factorization of 3 = 3</p>

103 <p>Prime factorization of 3 = 3</p>

105 <p>Prime factorization of 5 = 5</p>

104 <p>Prime factorization of 5 = 5</p>

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

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

107 <p>LCM (3,5,6) = 30 </p>

106 <p>LCM (3,5,6) = 30 </p>

108 <h2>Important glossaries for the LCM of 3,6 and 8</h2>

107 <h2>Important glossaries for the LCM of 3,6 and 8</h2>

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

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

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

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

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

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

112 </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>

111 </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>

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

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

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

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

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

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

116 <p>▶</p>

115 <p>▶</p>

117 <h2>Hiralee Lalitkumar Makwana</h2>

116 <h2>Hiralee Lalitkumar Makwana</h2>

118 <h3>About the Author</h3>

117 <h3>About the Author</h3>

119 <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>

118 <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>

120 <h3>Fun Fact</h3>

119 <h3>Fun Fact</h3>

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

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