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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 6 and 18. LCM helps to solve problems with fractions and scenarios like scheduling or aligning repeating cycles of events.</p>

4 <h2>What is the LCM of 6 and 18?</h2>

5 <h2>How to find the LCM of 6 and 18 ?</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 6 and 18 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 6 = 6,12,18,…</p>

11 <p>Multiples of 18 = 18,36,…</p>

12 <p><strong>Step 2:</strong>Ascertain the smallest multiple from the listed multiples of 6 and 18. </p>

13 <p>The LCM (Least common multiple) of 6 and 18 is 18. i.e., 18 is divisible by 6 and 18 with no reminder. </p>

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16 <h3>LCM of 6 and 18 using the Prime Factorization method</h3>

15 <h3>LCM of 6 and 18 using the Prime Factorization method</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>Steps 1:</strong>Find the prime factors of the numbers:</p>

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

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

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

20 <p>Prime factorization of 18 = 2×3×3</p>

19 <p>Prime factorization of 18 = 2×3×3</p>

21 <p> <strong>Step 2:</strong>Take the highest power of each prime factor and multiply the ascertained factors to get the LCM: </p>

20 <p> <strong>Step 2:</strong>Take the highest power of each prime factor and multiply the ascertained factors to get the LCM: </p>

22 <p>LCM (6,18) = 18</p>

21 <p>LCM (6,18) = 18</p>

23 <h3>LCM of 6 and 18 using the Division Method</h3>

22 <h3>LCM of 6 and 18 using the Division Method</h3>

24 <p>The Division Method involves dividing the numbers by their prime factors and multiplying the divisors to get the LCM. </p>

23 <p>The Division Method involves dividing the numbers by their prime factors and multiplying the divisors to get the LCM. </p>

25 <p><strong>Step1</strong>:Write down the numbers in a row;</p>

24 <p><strong>Step1</strong>:Write down the numbers in a row;</p>

26 <p><strong> Step</strong><strong>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. </p>

25 <p><strong> Step</strong><strong>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. </p>

27 <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 prime number.</p>

26 <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 prime number.</p>

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

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

29 <h2>Common Mistakes and how to avoid them while finding the LCM of 6 and 18</h2>

28 <h2>Common Mistakes and how to avoid them while finding the LCM of 6 and 18</h2>

30 <p>Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 6 and 18, make a note while practising. </p>

29 <p>Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 6 and 18, make a note while practising. </p>

31 <h3>Problem 1</h3>

30 <h3>Problem 1</h3>

32 <p>The LCM of a and b is 36. Given a is 6, find b.</p>

31 <p>The LCM of a and b is 36. Given a is 6, find b.</p>

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

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

34 <p>b is possibly one of 12,18 and 36. </p>

33 <p>b is possibly one of 12,18 and 36. </p>

35 <h3>Explanation</h3>

34 <h3>Explanation</h3>

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

35 <p>Using the formula; </p>

37 <p>LCM(a,b) =a×b/HCF(a,b) </p>

36 <p>LCM(a,b) =a×b/HCF(a,b) </p>

38 <p>a =6, b= ?</p>

37 <p>a =6, b= ?</p>

39 <p>LCM (a, b) = 36 </p>

38 <p>LCM (a, b) = 36 </p>

40 <p>The factors of 6 (a) are - 1,2,3,6; so we can assume that the HCF is one of these numbers. </p>

39 <p>The factors of 6 (a) are - 1,2,3,6; so we can assume that the HCF is one of these numbers. </p>

41 <p>By testing the values, we find the possible values of b. </p>

40 <p>By testing the values, we find the possible values of b. </p>

42 <p>Testing for 6; </p>

41 <p>Testing for 6; </p>

43 <p>36 = 6×b/6 </p>

42 <p>36 = 6×b/6 </p>

44 <p>b = 36 </p>

43 <p>b = 36 </p>

45 <p>Testing for 3; </p>

44 <p>Testing for 3; </p>

46 <p>36 = 6×b/3 </p>

45 <p>36 = 6×b/3 </p>

47 <p>b = 18 </p>

46 <p>b = 18 </p>

48 <p>Testing for 2; </p>

47 <p>Testing for 2; </p>

49 <p>36 = 6×b/2 </p>

48 <p>36 = 6×b/2 </p>

50 <p>b = 12 </p>

49 <p>b = 12 </p>

51 <p>Testing for 1; </p>

50 <p>Testing for 1; </p>

52 <p>36 =6×b/1 </p>

51 <p>36 =6×b/1 </p>

53 <p>b = 6 → cannot be true, as the LCM of 6,6 is 6. </p>

52 <p>b = 6 → cannot be true, as the LCM of 6,6 is 6. </p>

54 <p>Well explained 👍</p>

53 <p>Well explained 👍</p>

55 <h3>Problem 2</h3>

54 <h3>Problem 2</h3>

56 <p>If the HCF of 6 and 18 is 6, using the relationship between 6 and 18, find the LCM.</p>

55 <p>If the HCF of 6 and 18 is 6, using the relationship between 6 and 18, find the LCM.</p>

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

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

58 <p>Given values; </p>

57 <p>Given values; </p>

59 <p>HCF = 6</p>

58 <p>HCF = 6</p>

60 <p>a = 6 </p>

59 <p>a = 6 </p>

61 <p>b = 18</p>

60 <p>b = 18</p>

62 <p>Using the formula; </p>

61 <p>Using the formula; </p>

63 <p>LCM (a,b)=a×b/HCF(a, b)</p>

62 <p>LCM (a,b)=a×b/HCF(a, b)</p>

64 <p>LCM (6,18)= 6×18/6 =18</p>

63 <p>LCM (6,18)= 6×18/6 =18</p>

65 <h3>Explanation</h3>

64 <h3>Explanation</h3>

66 <p> The relationship between HCF and LCM, as explained above allows us to find the LCM without direct calculation. </p>

65 <p> The relationship between HCF and LCM, as explained above allows us to find the LCM without direct calculation. </p>

67 <p>Well explained 👍</p>

66 <p>Well explained 👍</p>

68 <h3>Problem 3</h3>

67 <h3>Problem 3</h3>

69 <p>Trains A and B arrive every 6 minutes and 18 minutes at the station at the same time. In how long will they arrive together again?</p>

68 <p>Trains A and B arrive every 6 minutes and 18 minutes at the station at the same time. In how long will they arrive together again?</p>

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

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

71 <p> The LCM of 6 and 18 =18. </p>

70 <p> The LCM of 6 and 18 =18. </p>

72 <h3>Explanation</h3>

71 <h3>Explanation</h3>

73 <p>The smallest common multiple is ascertained between the numbers to ascertain the next arrival of the trains at the same time, which is in 18 minutes. </p>

72 <p>The smallest common multiple is ascertained between the numbers to ascertain the next arrival of the trains at the same time, which is in 18 minutes. </p>

74 <p>Well explained 👍</p>

73 <p>Well explained 👍</p>

75 <h2>FAQ’s on LCM of 6 and 18</h2>

74 <h2>FAQ’s on LCM of 6 and 18</h2>

76 <h3>1.What is the HCF of 6 and 18?</h3>

75 <h3>1.What is the HCF of 6 and 18?</h3>

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

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

78 <p>Factors of 18 = 1,2,3,6,9,18</p>

77 <p>Factors of 18 = 1,2,3,6,9,18</p>

79 <p>HCF(6,18) = 6 </p>

78 <p>HCF(6,18) = 6 </p>

80 <h3>2.What are the factors of 6 and 18?</h3>

79 <h3>2.What are the factors of 6 and 18?</h3>

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

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

82 <p>Factors of 18 = 1,2,3,6,9,18</p>

81 <p>Factors of 18 = 1,2,3,6,9,18</p>

83 <p>Common factors: 1,2,3,6 </p>

82 <p>Common factors: 1,2,3,6 </p>

84 <h3>3.Is 6 a factor of 69?</h3>

83 <h3>3.Is 6 a factor of 69?</h3>

85 <p>No, 6 is not a factor of 69. When divided, a<a>remainder</a>is left behind. </p>

84 <p>No, 6 is not a factor of 69. When divided, a<a>remainder</a>is left behind. </p>

86 <h3>4.What is the LCM of 3,6 and 18?</h3>

85 <h3>4.What is the LCM of 3,6 and 18?</h3>

87 <ul><li>Prime factorization of 3 = 3 </li>

86 <ul><li>Prime factorization of 3 = 3 </li>

88 </ul><ul><li>Prime factorization of 6 = 2×3</li>

87 </ul><ul><li>Prime factorization of 6 = 2×3</li>

89 </ul><ul><li>Prime factorization of 18 = 3×3×2</li>

88 </ul><ul><li>Prime factorization of 18 = 3×3×2</li>

90 </ul><ul><li>LCM (3,6,18) = 18</li>

89 </ul><ul><li>LCM (3,6,18) = 18</li>

91 </ul><h3>5.Is 6 a factor of 0?</h3>

90 </ul><h3>5.Is 6 a factor of 0?</h3>

92 <p>Yes, 6 is a factor of 0. In fact, all non-zero numbers are factors of 0. </p>

91 <p>Yes, 6 is a factor of 0. In fact, all non-zero numbers are factors of 0. </p>

93 <h2>Important glossaries for LCM of 6 and 18</h2>

92 <h2>Important glossaries for LCM of 6 and 18</h2>

94 <p><strong>Multiple:</strong>A number and any integer multiplied.</p>

93 <p><strong>Multiple:</strong>A number and any integer multiplied.</p>

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

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

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

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

97 <p><strong>Co-prime numbers:</strong>When the only positive integer that is a divisor of them both is 1, a number is co-prime. </p>

96 <p><strong>Co-prime numbers:</strong>When the only positive integer that is a divisor of them both is 1, a number is co-prime. </p>

98 <p><strong>Relatively Prime Numbers:</strong>Numbers that have no common factors other than 1.</p>

97 <p><strong>Relatively Prime Numbers:</strong>Numbers that have no common factors other than 1.</p>

99 <p><strong>Fraction:</strong>A representation of a part of a whole. </p>

98 <p><strong>Fraction:</strong>A representation of a part of a whole. </p>

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

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

101 <p>▶</p>

100 <p>▶</p>

102 <h2>Hiralee Lalitkumar Makwana</h2>

101 <h2>Hiralee Lalitkumar Makwana</h2>

103 <h3>About the Author</h3>

102 <h3>About the Author</h3>

104 <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 <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>

105 <h3>Fun Fact</h3>

104 <h3>Fun Fact</h3>

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

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