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

3 <p>LCM is applied in most everyday tasks like planning, aligning events and even in alarms which is used literally every day. In this article, let us learn more about the LCM of 9,12 and 18.</p>

4 <h2>What is the LCM of 9,12 and 18?</h2>

5 <p>The LCM of 9,12 and 18 is 36. How did we find this? Let us learn! </p>

6 <h2>How to find the LCM of 9,12 and 18?</h2>

7 <h3>LCM of 9,12 and 18 using the Division method</h3>

8 <p>In this method, we list the multiples of the<a>numbers</a>given until we land at the smallest multiple that is common between the numbers. </p>

9 <p>To elaborate; </p>

10 <p>Multiples of 9 = 9,18,27,36,…</p>

11 <p>Multiples of 12 = 12,24,36,…</p>

12 <p>Multiples of 18 = 18,36,...</p>

13 <p>From the above we can clearly see that the smallest<a>common multiple</a>between the numbers is 36, which is the LCM of 9,12 and 18. </p>

14 <p>LCM (9,12,18) = 36 </p>

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17 <h3>LCM of 9,12 and 18 using the prime factorization method</h3>

16 <h3>LCM of 9,12 and 18 using the prime factorization method</h3>

18 <p>Here, we factorize the numbers into their prime<a>factor</a>and multiply the highest<a>powers</a>to find the LCM. </p>

17 <p>Here, we factorize the numbers into their prime<a>factor</a>and multiply the highest<a>powers</a>to find the LCM. </p>

19 <p>Substantiating the above; </p>

18 <p>Substantiating the above; </p>

20 <p><strong>Step 1.</strong>Prime factorize the numbers,</p>

19 <p><strong>Step 1.</strong>Prime factorize the numbers,</p>

21 <p>9 = 3×3</p>

20 <p>9 = 3×3</p>

22 <p>12 = 2×2×3</p>

21 <p>12 = 2×2×3</p>

23 <p>18= 2×3×3</p>

22 <p>18= 2×3×3</p>

24 <p><strong>Step 2.</strong>Multiply the highest powers </p>

23 <p><strong>Step 2.</strong>Multiply the highest powers </p>

25 <p><strong>Step 3.</strong>Multiply the factors to get the LCM </p>

24 <p><strong>Step 3.</strong>Multiply the factors to get the LCM </p>

26 <p>LCM(9,12,18) = 36 </p>

25 <p>LCM(9,12,18) = 36 </p>

27 <h3>LCM of 9,12 and 18 using the division method</h3>

26 <h3>LCM of 9,12 and 18 using the division method</h3>

28 <p>In the division method, </p>

27 <p>In the division method, </p>

29 <p><strong>Step 1:</strong>Write the given numbers in a row </p>

28 <p><strong>Step 1:</strong>Write the given numbers in a row </p>

30 <p><strong>Step 2:</strong>proceed with the division of numbers with a factor that is divisible by at least one of the numbers. </p>

29 <p><strong>Step 2:</strong>proceed with the division of numbers with a factor that is divisible by at least one of the numbers. </p>

31 <p><strong>Step 3:</strong>Carry forward the numbers that haven’t been divided earlier. </p>

30 <p><strong>Step 3:</strong>Carry forward the numbers that haven’t been divided earlier. </p>

32 <p><strong>Step 4:</strong>Continue dividing till the<a>remainder</a>is 1 for all the numbers. </p>

31 <p><strong>Step 4:</strong>Continue dividing till the<a>remainder</a>is 1 for all the numbers. </p>

33 <p><strong>Step 5:</strong>Multiply the divisors in the first column to find the LCM. </p>

32 <p><strong>Step 5:</strong>Multiply the divisors in the first column to find the LCM. </p>

34 <p><strong>Step 6:</strong>LCM (9,12,18) = 36 </p>

33 <p><strong>Step 6:</strong>LCM (9,12,18) = 36 </p>

35 <h2>Common mistakes and how to avoid them in LCM of 9,12 and 18</h2>

34 <h2>Common mistakes and how to avoid them in LCM of 9,12 and 18</h2>

36 <p>Listed here are a few common mistakes that one may commit while trying to find the LCM of 9,12 and 18, make a note while practicing. </p>

35 <p>Listed here are a few common mistakes that one may commit while trying to find the LCM of 9,12 and 18, make a note while practicing. </p>

37 <h3>Problem 1</h3>

36 <h3>Problem 1</h3>

38 <p>LCM(9,12) = 36, LCM (9,12,x) is also 36. Find x.</p>

37 <p>LCM(9,12) = 36, LCM (9,12,x) is also 36. Find x.</p>

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

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

40 <p>The possible values of x could be → 1,2,3,4,6,9,12,18 or 36. </p>

39 <p>The possible values of x could be → 1,2,3,4,6,9,12,18 or 36. </p>

41 <h3>Explanation</h3>

40 <h3>Explanation</h3>

42 <p>The LCM of the numbers 9 and 12 is 36 and for the LCM to still remain as 36 after a number is included, i.e., 9,12,x; it must be a divisor of the number 36. The possible number of x is going to be a divisor of 36. Therefore, the possible values could be the above listed divisors. </p>

41 <p>The LCM of the numbers 9 and 12 is 36 and for the LCM to still remain as 36 after a number is included, i.e., 9,12,x; it must be a divisor of the number 36. The possible number of x is going to be a divisor of 36. Therefore, the possible values could be the above listed divisors. </p>

43 <p>Well explained 👍</p>

42 <p>Well explained 👍</p>

44 <h3>Problem 2</h3>

43 <h3>Problem 2</h3>

45 <p>Find x, LCM (99,12,x) = 36.</p>

44 <p>Find x, LCM (99,12,x) = 36.</p>

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

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

47 <p>We know the LCM of 9,12 = 36 </p>

46 <p>We know the LCM of 9,12 = 36 </p>

48 <p>Prime factorization of 36 36 = 3×3×2×2 </p>

47 <p>Prime factorization of 36 36 = 3×3×2×2 </p>

49 <p>The LCM of 3,9 already includes 32 and 22, and the factor of x must include the same, which means the factors of 36 are likely the value of x → 1,2,3,6,12,18,36. </p>

48 <p>The LCM of 3,9 already includes 32 and 22, and the factor of x must include the same, which means the factors of 36 are likely the value of x → 1,2,3,6,12,18,36. </p>

50 <h3>Explanation</h3>

49 <h3>Explanation</h3>

51 <p>By following the above assumption we can assume that the value of x is one of 1,2,3,6,12,18,36. </p>

50 <p>By following the above assumption we can assume that the value of x is one of 1,2,3,6,12,18,36. </p>

52 <p>Well explained 👍</p>

51 <p>Well explained 👍</p>

53 <h3>Problem 3</h3>

52 <h3>Problem 3</h3>

54 <p>Prove that LCM(a², b²) = LCM(a, b)² in a case where ‘a’ and ‘b’ are co-prime. Apply to find the LCM(9²,12²).</p>

53 <p>Prove that LCM(a², b²) = LCM(a, b)² in a case where ‘a’ and ‘b’ are co-prime. Apply to find the LCM(9²,12²).</p>

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

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

56 <p>We can tell that 9 and 12 are not coprime, they have more factors than just 1 and themselves. To make it so, we prime factorize them; </p>

55 <p>We can tell that 9 and 12 are not coprime, they have more factors than just 1 and themselves. To make it so, we prime factorize them; </p>

57 <p>9 = 32</p>

56 <p>9 = 32</p>

58 <p>12 = 22×3 </p>

57 <p>12 = 22×3 </p>

59 <p>Now we find their squares; </p>

58 <p>Now we find their squares; </p>

60 <p>92 = 34 = 81</p>

59 <p>92 = 34 = 81</p>

61 <p>122 =24×32 = 144</p>

60 <p>122 =24×32 = 144</p>

62 <p>We now use the formula for prime factors; </p>

61 <p>We now use the formula for prime factors; </p>

63 <p>LCM(92,122) = LCM(34,24×32) </p>

62 <p>LCM(92,122) = LCM(34,24×32) </p>

64 <p>= 24×34 </p>

63 <p>= 24×34 </p>

65 <p>= 16×81 </p>

64 <p>= 16×81 </p>

66 <p>= 1296 </p>

65 <p>= 1296 </p>

67 <h3>Explanation</h3>

66 <h3>Explanation</h3>

68 <p>The formula LCM(a2, b2) = LCM(a, b)2 holds good. The LCM of 92 and 122 is 1296. </p>

67 <p>The formula LCM(a2, b2) = LCM(a, b)2 holds good. The LCM of 92 and 122 is 1296. </p>

69 <p>Well explained 👍</p>

68 <p>Well explained 👍</p>

70 <h2>FAQs on the LCM of 9,12 and 18</h2>

69 <h2>FAQs on the LCM of 9,12 and 18</h2>

71 <h3>1.What is the LCM of 9,12,18,36?</h3>

70 <h3>1.What is the LCM of 9,12,18,36?</h3>

72 <p>Prime factorize the numbers;</p>

71 <p>Prime factorize the numbers;</p>

73 <p>9 = 3×3</p>

72 <p>9 = 3×3</p>

74 <p>12 = 2×2×3</p>

73 <p>12 = 2×2×3</p>

75 <p>18 = 3×3×2</p>

74 <p>18 = 3×3×2</p>

76 <p>36 = 2×2×3×3 </p>

75 <p>36 = 2×2×3×3 </p>

77 <p>LCM(9,12,18,36) = 36 </p>

76 <p>LCM(9,12,18,36) = 36 </p>

78 <h3>2.What is the LCM of 9,12,18, 24 and 27?</h3>

77 <h3>2.What is the LCM of 9,12,18, 24 and 27?</h3>

79 <p>Prime factorize the numbers; </p>

78 <p>Prime factorize the numbers; </p>

80 <p>9 = 3×3</p>

79 <p>9 = 3×3</p>

81 <p>12 = 2×2×3</p>

80 <p>12 = 2×2×3</p>

82 <p>18 = 3×3×2</p>

81 <p>18 = 3×3×2</p>

83 <p>24 = 2×2×3×2 </p>

82 <p>24 = 2×2×3×2 </p>

84 <p>27= 3×3×3</p>

83 <p>27= 3×3×3</p>

85 <p>LCM(9,12,18,24,27) = 648 </p>

84 <p>LCM(9,12,18,24,27) = 648 </p>

86 <h3>3.What is the HCF of 9,12,18 and 21?</h3>

85 <h3>3.What is the HCF of 9,12,18 and 21?</h3>

87 <p>List the<a>common factors</a>of the numbers given;</p>

86 <p>List the<a>common factors</a>of the numbers given;</p>

88 <p>Factors of 9 = 1,3,9 </p>

87 <p>Factors of 9 = 1,3,9 </p>

89 <p>Factors of 12 = 1,2,3,4,6,12</p>

88 <p>Factors of 12 = 1,2,3,4,6,12</p>

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

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

91 <p>Factors of 21 = 1,3,7,21</p>

90 <p>Factors of 21 = 1,3,7,21</p>

92 <p>HCF(9,12,18,21) = 3 </p>

91 <p>HCF(9,12,18,21) = 3 </p>

93 <h3>4.What is the LCM of 9,12 and 15?</h3>

92 <h3>4.What is the LCM of 9,12 and 15?</h3>

94 <p>Prime factorize the numbers; </p>

93 <p>Prime factorize the numbers; </p>

95 <p>9 = 3×3</p>

94 <p>9 = 3×3</p>

96 <p>12 = 2×2×3</p>

95 <p>12 = 2×2×3</p>

97 <p>15 = 3×5</p>

96 <p>15 = 3×5</p>

98 <p>LCM (9,12,15) = 180 </p>

97 <p>LCM (9,12,15) = 180 </p>

99 <h3>5.What is the GCF of 15 and 60?</h3>

98 <h3>5.What is the GCF of 15 and 60?</h3>

100 <p>List the common factors of the numbers given; </p>

99 <p>List the common factors of the numbers given; </p>

101 <p>Factors of 15 = 1,3,5,15</p>

100 <p>Factors of 15 = 1,3,5,15</p>

102 <p>Factors of 60 = 1,2,3,4,5,6,10,12,15,20,30,60 </p>

101 <p>Factors of 60 = 1,2,3,4,5,6,10,12,15,20,30,60 </p>

103 <p>HCF(15,60) = 15 </p>

102 <p>HCF(15,60) = 15 </p>

104 <h2>Important glossaries for the LCM of 9,12 and 18</h2>

103 <h2>Important glossaries for the LCM of 9,12 and 18</h2>

105 <ul><li><strong>Multiple</strong>- It is a product of a number and any natural integer. So for 18; 18,36,54 are the multiples.</li>

104 <ul><li><strong>Multiple</strong>- It is a product of a number and any natural integer. So for 18; 18,36,54 are the multiples.</li>

106 </ul><ul><li><strong>Prime Factor</strong>- It is a prime number that one gets after factorization of any given number. Like for 12; 1,2,3,4,6 and 12 are prime factors as they can be divided by 1 or the number itself.</li>

105 </ul><ul><li><strong>Prime Factor</strong>- It is a prime number that one gets after factorization of any given number. Like for 12; 1,2,3,4,6 and 12 are prime factors as they can be divided by 1 or the number itself.</li>

107 </ul><ul><li><strong>Prime Factorization</strong>- It is a process of dividing the number into prime factors.</li>

106 </ul><ul><li><strong>Prime Factorization</strong>- It is a process of dividing the number into prime factors.</li>

108 </ul><ul><li><strong>Co-prime numbers</strong>- These are the positive integers, where both the numbers can be divided only by 1. </li>

107 </ul><ul><li><strong>Co-prime numbers</strong>- These are the positive integers, where both the numbers can be divided only by 1. </li>

109 </ul><ul><li><strong>Fraction</strong>- It is expressed as part of a whole, in which the numerator is divided by the denominator, so for a fraction like 18/9- 18 is the numerator and 9 is the denominator. Proper fraction is where numerator is always lesser than denominator. </li>

108 </ul><ul><li><strong>Fraction</strong>- It is expressed as part of a whole, in which the numerator is divided by the denominator, so for a fraction like 18/9- 18 is the numerator and 9 is the denominator. Proper fraction is where numerator is always lesser than denominator. </li>

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

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

111 <p>▶</p>

110 <p>▶</p>

112 <h2>Hiralee Lalitkumar Makwana</h2>

111 <h2>Hiralee Lalitkumar Makwana</h2>

113 <h3>About the Author</h3>

112 <h3>About the Author</h3>

114 <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>

113 <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>

115 <h3>Fun Fact</h3>

114 <h3>Fun Fact</h3>

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

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