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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 12 and 18. 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>

4 <h2>What is the LCM of 12 and 18?</h2>

5 <h2>How to Find the LCM of 12 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 12 and 18 using the Listing Multiples Method</h3>

8 <p>The LCM of 12 and 18 can be found using the following steps:</p>

9 <p><strong>Steps:</strong></p>

10 <ol><li>List the multiples of each number</li>

11 </ol><p> - Multiples of 12 = 12, 24, 36, 48, 60, 72, …</p>

12 <p> - Multiples of 18 = 18, 36, 54, 72, 90, …</p>

13 <ol><li>Figure the smallest multiple from the listed multiples</li>

14 </ol><p> - The smallest<a>common multiple</a>is 36.</p>

15 <p>Thus, LCM(12, 18) = 36</p>

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18 <h3>LCM of 12 and 18 using the Prime Factorization Method</h3>

17 <h3>LCM of 12 and 18 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><strong>Steps:</strong></p>

19 <p><strong>Steps:</strong></p>

21 <ol><li><strong>Devise prime factors of the given numbers:</strong></li>

20 <ol><li><strong>Devise prime factors of the given numbers:</strong></li>

22 </ol><p> - Prime factorization of 12 = 2 × 2 × 3</p>

21 </ol><p> - Prime factorization of 12 = 2 × 2 × 3</p>

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

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

24 <ol><li><strong> Pick the highest powers of each prime factor:</strong></li>

23 <ol><li><strong> Pick the highest powers of each prime factor:</strong></li>

25 </ol><p> - Highest power of 2 = 2²</p>

24 </ol><p> - Highest power of 2 = 2²</p>

26 <p> - Highest power of 3 = 3²</p>

25 <p> - Highest power of 3 = 3²</p>

27 <ol><li><strong> Find the<a>product</a>of the highest powers to get the LCM:</strong></li>

26 <ol><li><strong> Find the<a>product</a>of the highest powers to get the LCM:</strong></li>

28 </ol><p> LCM(12, 18) = 2² × 3² = 36.</p>

27 </ol><p> LCM(12, 18) = 2² × 3² = 36.</p>

29 <h3>LCM of 12 and 18 using the Division Method</h3>

28 <h3>LCM of 12 and 18 using the Division Method</h3>

30 <p>This method involves dividing both numbers by their common prime factors until no further division is possible, then multiplying the divisors to get the LCM.</p>

29 <p>This method involves dividing both numbers by their common prime factors until no further division is possible, then multiplying the divisors to get the LCM.</p>

31 <p><strong>Steps:</strong></p>

30 <p><strong>Steps:</strong></p>

32 <ol><li> Write the numbers: </li>

31 <ol><li> Write the numbers: </li>

33 </ol><ol><li>Divide by common prime factors and multiply the divisors:</li>

32 </ol><ol><li>Divide by common prime factors and multiply the divisors:</li>

34 </ol><p> - 2 × 2 × 3 × 3 = 36</p>

33 </ol><p> - 2 × 2 × 3 × 3 = 36</p>

35 <p>Thus, LCM(12, 18) = 36.</p>

34 <p>Thus, LCM(12, 18) = 36.</p>

36 <h2>Common Mistakes and how to avoid them while finding the LCM of 12 and 18</h2>

35 <h2>Common Mistakes and how to avoid them while finding the LCM of 12 and 18</h2>

37 <p>Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 3 and 9, make a note while practicing.</p>

36 <p>Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 3 and 9, make a note while practicing.</p>

38 <h3>Problem 1</h3>

37 <h3>Problem 1</h3>

39 <p>Goods are received by a shipping company every 12 and 18 days. If the shipments have been received today, when will they next arrive at, the same day?</p>

38 <p>Goods are received by a shipping company every 12 and 18 days. If the shipments have been received today, when will they next arrive at, the same day?</p>

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

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

41 <p>The LCM of 12 and 18 is 36.</p>

40 <p>The LCM of 12 and 18 is 36.</p>

42 <h3>Explanation</h3>

41 <h3>Explanation</h3>

43 <p>The goods will be received next in 36 days. 36 is the LCM of 12 and 18, which is the smallest time interval between the digits.</p>

42 <p>The goods will be received next in 36 days. 36 is the LCM of 12 and 18, which is the smallest time interval between the digits.</p>

44 <p>Well explained 👍</p>

43 <p>Well explained 👍</p>

45 <h3>Problem 2</h3>

44 <h3>Problem 2</h3>

46 <p>A maintenance schedule for projectors is set up every 12 weeks and 18 weeks at a school. If both the projectors are serviced today, in how many weeks will they be serviced again on the same day?</p>

45 <p>A maintenance schedule for projectors is set up every 12 weeks and 18 weeks at a school. If both the projectors are serviced today, in how many weeks will they be serviced again on the same day?</p>

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

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

48 <p>The LCM of 12 and 18 is 36.</p>

47 <p>The LCM of 12 and 18 is 36.</p>

49 <h3>Explanation</h3>

48 <h3>Explanation</h3>

50 <p>Both projectors will need maintenance again in 36 weeks.36 is the LCM of 12 and 18, which is the smallest time interval between the digits.</p>

49 <p>Both projectors will need maintenance again in 36 weeks.36 is the LCM of 12 and 18, which is the smallest time interval between the digits.</p>

51 <p>Well explained 👍</p>

50 <p>Well explained 👍</p>

52 <h3>Problem 3</h3>

51 <h3>Problem 3</h3>

53 <p>Two clocks strike every 12 hours and 18 hours. If both of them strike now, when will they next strike together?</p>

52 <p>Two clocks strike every 12 hours and 18 hours. If both of them strike now, when will they next strike together?</p>

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

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

55 <p>The LCM of 12 and 18 is 36.</p>

54 <p>The LCM of 12 and 18 is 36.</p>

56 <h3>Explanation</h3>

55 <h3>Explanation</h3>

57 <p>Both clocks will chime together again in 36 hours. 36 is the LCM of 12 and 18, which is the smallest time interval between the digits.</p>

56 <p>Both clocks will chime together again in 36 hours. 36 is the LCM of 12 and 18, which is the smallest time interval between the digits.</p>

58 <p>Well explained 👍</p>

57 <p>Well explained 👍</p>

59 <h3>Problem 4</h3>

58 <h3>Problem 4</h3>

60 <p>In a neighborhood park, the fountain show is turned on every 12 minutes, and the light show every 18 minutes. If both the shows are turned on at the same time, when will they next be turned on together again?</p>

59 <p>In a neighborhood park, the fountain show is turned on every 12 minutes, and the light show every 18 minutes. If both the shows are turned on at the same time, when will they next be turned on together again?</p>

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

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

62 <p>The LCM of 12 and 18 is 36.</p>

61 <p>The LCM of 12 and 18 is 36.</p>

63 <h3>Explanation</h3>

62 <h3>Explanation</h3>

64 <p>Both the shows will turn on at the same time in 36 minutes, 36 is the LCM of 12 and 18, which is the smallest time interval between the digits.</p>

63 <p>Both the shows will turn on at the same time in 36 minutes, 36 is the LCM of 12 and 18, which is the smallest time interval between the digits.</p>

65 <p>Well explained 👍</p>

64 <p>Well explained 👍</p>

66 <h3>Problem 5</h3>

65 <h3>Problem 5</h3>

67 <p>A car mechanic services a red car every 12 days and a blue car every 18 days. If the cars are serviced today, when will they be serviced next together?</p>

66 <p>A car mechanic services a red car every 12 days and a blue car every 18 days. If the cars are serviced today, when will they be serviced next together?</p>

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

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

69 <p>The LCM of 12 and 18 is 36.</p>

68 <p>The LCM of 12 and 18 is 36.</p>

70 <h3>Explanation</h3>

69 <h3>Explanation</h3>

71 <p>Both cars will be serviced again in 36 days. 36 is the LCM of 12 and 18, which is the smallest time interval between the digits.</p>

70 <p>Both cars will be serviced again in 36 days. 36 is the LCM of 12 and 18, which is the smallest time interval between the digits.</p>

72 <p>Well explained 👍</p>

71 <p>Well explained 👍</p>

73 <h2>FAQs on LCM of 12 and 18</h2>

72 <h2>FAQs on LCM of 12 and 18</h2>

74 <h3>1.Why is the LCM of 12 and 18 not simply their product (12 × 18 = 216)?</h3>

73 <h3>1.Why is the LCM of 12 and 18 not simply their product (12 × 18 = 216)?</h3>

75 <p>Multiplying gives you the product of the numbers, in this case,216. LCM, however, is the smallest common multiple that can be ascertained following the listing multiples method, prime factorization, or the division method.</p>

74 <p>Multiplying gives you the product of the numbers, in this case,216. LCM, however, is the smallest common multiple that can be ascertained following the listing multiples method, prime factorization, or the division method.</p>

76 <h3>2.How do you find the LCM of 12 and 18 using a Venn diagram?</h3>

75 <h3>2.How do you find the LCM of 12 and 18 using a Venn diagram?</h3>

77 <p>Follow the below steps to ascertain the LCM of 10 and 12 using a Venn diagram;</p>

76 <p>Follow the below steps to ascertain the LCM of 10 and 12 using a Venn diagram;</p>

78 <p>List the prime factors of the digits </p>

77 <p>List the prime factors of the digits </p>

79 <p> - Prime factorization of 12 = 2 × 2 × 3 → 2×3</p>

78 <p> - Prime factorization of 12 = 2 × 2 × 3 → 2×3</p>

80 <p> - Prime factorization of 18 = 2 × 3 × 3 → 2×32</p>

79 <p> - Prime factorization of 18 = 2 × 3 × 3 → 2×32</p>

81 <p>Place the factors in the diagram</p>

80 <p>Place the factors in the diagram</p>

82 <ul><li>2 and 3 are<a>common factors</a>, place it in the overlapping section. </li>

81 <ul><li>2 and 3 are<a>common factors</a>, place it in the overlapping section. </li>

83 <li>2,3 are unique factors ascertained after the common factor for 12 and 18. Place them in their own section. </li>

82 <li>2,3 are unique factors ascertained after the common factor for 12 and 18. Place them in their own section. </li>

84 <li>Now, multiply both the common and the unique factors - 2 × 2 × 3×3 = 36</li>

83 <li>Now, multiply both the common and the unique factors - 2 × 2 × 3×3 = 36</li>

85 <li>The LCM (12,18) = 36. </li>

84 <li>The LCM (12,18) = 36. </li>

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

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

87 <p>The LCM can be found using the<a>formula</a>, and as explained with the example given below. </p>

86 <p>The LCM can be found using the<a>formula</a>, and as explained with the example given below. </p>

88 <p>LCM (a, b)= a×b/HCF(a, b)</p>

87 <p>LCM (a, b)= a×b/HCF(a, b)</p>

89 <p>For 12 and 18, HCF(12,18)= 6</p>

88 <p>For 12 and 18, HCF(12,18)= 6</p>

90 <p>So, LCM(12,18)=12×18/6 = 36</p>

89 <p>So, LCM(12,18)=12×18/6 = 36</p>

91 <h3>4.If both the numbers are prime, what is the LCM? Explain in the case of 12 and 18. </h3>

90 <h3>4.If both the numbers are prime, what is the LCM? Explain in the case of 12 and 18. </h3>

92 <p>If both the numbers are prime, their LCM will be the product of the numbers as they do not share any common factors but 1. However, 12 and 18 are non-<a>prime numbers</a>/<a>composite numbers</a>, i.e, they share a common factor, therefore their LCM is 36.</p>

91 <p>If both the numbers are prime, their LCM will be the product of the numbers as they do not share any common factors but 1. However, 12 and 18 are non-<a>prime numbers</a>/<a>composite numbers</a>, i.e, they share a common factor, therefore their LCM is 36.</p>

93 <h3>5.How can you check if the LCM you ascertained is right? Explain using the digits 12 and 18.</h3>

92 <h3>5.How can you check if the LCM you ascertained is right? Explain using the digits 12 and 18.</h3>

94 <p>The LCM ascertained can be verified in the following way; </p>

93 <p>The LCM ascertained can be verified in the following way; </p>

95 <p>- LCM of the numbers 12 and 18 is 36. </p>

94 <p>- LCM of the numbers 12 and 18 is 36. </p>

96 <p>- Divide the LCM with the digits, i.e., 36/12 = 3, 36/18 =2.</p>

95 <p>- Divide the LCM with the digits, i.e., 36/12 = 3, 36/18 =2.</p>

97 <p>- The results are<a>whole numbers</a>, i.e., there are no reminders left behind, therefore we can conclude the LCM ascertained is right.</p>

96 <p>- The results are<a>whole numbers</a>, i.e., there are no reminders left behind, therefore we can conclude the LCM ascertained is right.</p>

98 <h2>Important glossaries for the LCM of 12 and 18</h2>

97 <h2>Important glossaries for the LCM of 12 and 18</h2>

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

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

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

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

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

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

102 <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>

101 <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>

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

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

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

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

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

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

106 <p>▶</p>

105 <p>▶</p>

107 <h2>Hiralee Lalitkumar Makwana</h2>

106 <h2>Hiralee Lalitkumar Makwana</h2>

108 <h3>About the Author</h3>

107 <h3>About the Author</h3>

109 <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>

108 <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>

110 <h3>Fun Fact</h3>

109 <h3>Fun Fact</h3>

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

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