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1 - <p>282 Learners</p>

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

3 <p>The meaning of least common factor (LCM) is to find the smallest number that divides any two integers evenly. LCM is used mainly in fractions to find a common number for both the integers. We use LCM for solving problems, lining up cycles or even synchronizing of events, also to schedule tasks in everyday life.</p>

4 <h2>What is the LCM of 15 and 27?</h2>

5 <p>We use LCM<a>of</a>15 and 27 to find the smallest<a>number</a>that divides both the numbers equally. The smallest positive number is the number that divides both numbers equally, is 210 without leaving any<a>remainder</a>. LCM is used mainly in<a>fractions</a>to find a common number for both the<a>integers</a>. </p>

6 <h2>How to find the LCM of 15 and 27?</h2>

7 <h3>LCM of 15 and 27 using Division method:</h3>

8 <p>In division method, we divide both the numbers, we begin with dividing side by side the smallest number. We continue dividing until we get a common number that divides both the numbers equally. It makes it easier for the children to focus on prime<a>factors</a>and identify them.</p>

9 <ul><li>3 divides 15 and 27</li>

10 </ul><ul><li>5 divides 15 and not 27</li>

11 </ul><ul><li>9 divides 27 and not 15</li>

12 </ul><p>Now multiply the divisors : 3×5×9=135 which is the LCM. </p>

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15 <h3>LCM of 15 and 27 using Listing multiples:</h3>

14 <h3>LCM of 15 and 27 using Listing multiples:</h3>

16 <p>Start by listing multiples of both the numbers separately:</p>

15 <p>Start by listing multiples of both the numbers separately:</p>

17 <p>Multiples of 15 are 15,30,45,60,75,90,105,120,135…..</p>

16 <p>Multiples of 15 are 15,30,45,60,75,90,105,120,135…..</p>

18 <p>Multiples of 27 are 27,54,81,108,135…..</p>

17 <p>Multiples of 27 are 27,54,81,108,135…..</p>

19 <p>The least<a>common factor</a>from the list is 135. Therefore, the LCM of 15 and 27 is 135. </p>

18 <p>The least<a>common factor</a>from the list is 135. Therefore, the LCM of 15 and 27 is 135. </p>

20 <h3>LCM of 15 and 27 using Prime factorization:</h3>

19 <h3>LCM of 15 and 27 using Prime factorization:</h3>

21 <p>We part both the numbers unto factors:</p>

20 <p>We part both the numbers unto factors:</p>

22 <p>Factor of 15: 3×5</p>

21 <p>Factor of 15: 3×5</p>

23 <p>Factors of 27: 33</p>

22 <p>Factors of 27: 33</p>

24 <p>Take the<a>powers</a>of both the numbers and multiply together:</p>

23 <p>Take the<a>powers</a>of both the numbers and multiply together:</p>

25 <p>LCM=33x5=135. </p>

24 <p>LCM=33x5=135. </p>

26 <h2>Common Mistakes and How to Avoid Them in LCM of 15 and 27</h2>

25 <h2>Common Mistakes and How to Avoid Them in LCM of 15 and 27</h2>

27 <p>While solving problems based on the LCM of 15 and 27, children fail to understand few concepts, to give an idea of the mistakes, given below are a few mistakes and solutions of how to avoid them: </p>

26 <p>While solving problems based on the LCM of 15 and 27, children fail to understand few concepts, to give an idea of the mistakes, given below are a few mistakes and solutions of how to avoid them: </p>

28 <h3>Problem 1</h3>

27 <h3>Problem 1</h3>

29 <p>Find the LCM of 15 and x, if the LCM is 60. What is the value of X?</p>

28 <p>Find the LCM of 15 and x, if the LCM is 60. What is the value of X?</p>

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

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

31 <p>X=4.</p>

30 <p>X=4.</p>

32 <h3>Explanation</h3>

31 <h3>Explanation</h3>

33 <p>To add the fractions, we need to find the prime factorization of 15</p>

32 <p>To add the fractions, we need to find the prime factorization of 15</p>

34 <p> Prime factors of 15: 3 × 5</p>

33 <p> Prime factors of 15: 3 × 5</p>

35 <p>The LCM of 15 and X is given as 60.</p>

34 <p>The LCM of 15 and X is given as 60.</p>

36 <p> 60= 22 x3x5</p>

35 <p> 60= 22 x3x5</p>

37 <p>Since X shares factors with 60, the missing number should include 22 as 15 does not include any factor of 2.</p>

36 <p>Since X shares factors with 60, the missing number should include 22 as 15 does not include any factor of 2.</p>

38 <p>Therefore, </p>

37 <p>Therefore, </p>

39 <p>X=22=4.</p>

38 <p>X=22=4.</p>

40 <p>LCM of 15 and 4 is : </p>

39 <p>LCM of 15 and 4 is : </p>

41 <p>LCM(15,4)= 22 × 3 × 5 =60.</p>

40 <p>LCM(15,4)= 22 × 3 × 5 =60.</p>

42 <p>Thus, X=4. </p>

41 <p>Thus, X=4. </p>

43 <p>Well explained 👍</p>

42 <p>Well explained 👍</p>

44 <h3>Problem 2</h3>

43 <h3>Problem 2</h3>

45 <p>Given two pairs of numbers (12,18) and (15,24) which pair has the greater LCM?</p>

44 <p>Given two pairs of numbers (12,18) and (15,24) which pair has the greater LCM?</p>

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

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

47 <p>let us first find LCM of each pair:</p>

46 <p>let us first find LCM of each pair:</p>

48 <p>LCM of 12 and 18: </p>

47 <p>LCM of 12 and 18: </p>

49 <p>Factorization of 12= 22 × 3</p>

48 <p>Factorization of 12= 22 × 3</p>

50 <p>Factors of 18= 2x 32</p>

49 <p>Factors of 18= 2x 32</p>

51 <p>Take the highest powers of both the numbers:</p>

50 <p>Take the highest powers of both the numbers:</p>

52 <p>LCM(12,18)= 22 × 32 = 4 × 9=36</p>

51 <p>LCM(12,18)= 22 × 32 = 4 × 9=36</p>

53 <p>LCM of 15 and 24:</p>

52 <p>LCM of 15 and 24:</p>

54 <p>Factorization of 15= 3 × 5</p>

53 <p>Factorization of 15= 3 × 5</p>

55 <p>Factorization of 24= 23 × 3</p>

54 <p>Factorization of 24= 23 × 3</p>

56 <p>Take the highest powers of both the numbers:</p>

55 <p>Take the highest powers of both the numbers:</p>

57 <p>LCM(15,24)= 23 × 3 × 5= 8 × 15=120. </p>

56 <p>LCM(15,24)= 23 × 3 × 5= 8 × 15=120. </p>

58 <h3>Explanation</h3>

57 <h3>Explanation</h3>

59 <p>LCM(15,24)= 120</p>

58 <p>LCM(15,24)= 120</p>

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

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

61 <p>so, (15,24 has greater LCM</p>

60 <p>so, (15,24 has greater LCM</p>

62 <p>Well explained 👍</p>

61 <p>Well explained 👍</p>

63 <h3>Problem 3</h3>

62 <h3>Problem 3</h3>

64 <p>Simplify the fraction 15/27 by finding the LCM of the numerator and the denominator’s greatest common divisor(GCD).</p>

63 <p>Simplify the fraction 15/27 by finding the LCM of the numerator and the denominator’s greatest common divisor(GCD).</p>

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

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

66 <p>answer : 5/9</p>

65 <p>answer : 5/9</p>

67 <h3>Explanation</h3>

66 <h3>Explanation</h3>

68 <p>Prime Factorization of 15:</p>

67 <p>Prime Factorization of 15:</p>

69 <p>15=3 × 5</p>

68 <p>15=3 × 5</p>

70 <p>Prime Factorization of 27:</p>

69 <p>Prime Factorization of 27:</p>

71 <p>27=33</p>

70 <p>27=33</p>

72 <p>GCD of 15 and 27 is 3.</p>

71 <p>GCD of 15 and 27 is 3.</p>

73 <p>To simplify: </p>

72 <p>To simplify: </p>

74 <p>15/27 = 15÷3/27÷3 = 5/9.</p>

73 <p>15/27 = 15÷3/27÷3 = 5/9.</p>

75 <p>Well explained 👍</p>

74 <p>Well explained 👍</p>

76 <h3>Problem 4</h3>

75 <h3>Problem 4</h3>

77 <p>If the LCM of two numbers a and b is 72, and their GCD is 4. Find the product of a and b.</p>

76 <p>If the LCM of two numbers a and b is 72, and their GCD is 4. Find the product of a and b.</p>

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

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

79 <p>product of a and b =288</p>

78 <p>product of a and b =288</p>

80 <h3>Explanation</h3>

79 <h3>Explanation</h3>

81 <p>LCM(a, b) x GCD (a, b)= a × b</p>

80 <p>LCM(a, b) x GCD (a, b)= a × b</p>

82 <p>LCM(a, b)=72 and GCD(a, b)=4</p>

81 <p>LCM(a, b)=72 and GCD(a, b)=4</p>

83 <p>72 × 4= a × b</p>

82 <p>72 × 4= a × b</p>

84 <p>a × b =288.</p>

83 <p>a × b =288.</p>

85 <p>Well explained 👍</p>

84 <p>Well explained 👍</p>

86 <h3>Problem 5</h3>

85 <h3>Problem 5</h3>

87 <p>If a=18 and LCM of a and b is 90, find b.</p>

86 <p>If a=18 and LCM of a and b is 90, find b.</p>

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

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

89 <p>b=10.</p>

88 <p>b=10.</p>

90 <h3>Explanation</h3>

89 <h3>Explanation</h3>

91 <p> by using the formula:</p>

90 <p> by using the formula:</p>

92 <p>LCM(a, b)= a × b/GCD(a, b)</p>

91 <p>LCM(a, b)= a × b/GCD(a, b)</p>

93 <p>18=2x32 and the LCM is 90</p>

92 <p>18=2x32 and the LCM is 90</p>

94 <p>Factors of 90 are 2 × 32 × 5</p>

93 <p>Factors of 90 are 2 × 32 × 5</p>

95 <p>The missing factor is 5, so b =5 × 2 =10</p>

94 <p>The missing factor is 5, so b =5 × 2 =10</p>

96 <p>b=10.</p>

95 <p>b=10.</p>

97 <p>Well explained 👍</p>

96 <p>Well explained 👍</p>

98 <h2>FAQs on LCM of 15 and 27</h2>

97 <h2>FAQs on LCM of 15 and 27</h2>

99 <h3>1.What is the LCM of 18 and 27?</h3>

98 <h3>1.What is the LCM of 18 and 27?</h3>

100 <p>The LCM of 18 and 27 is 54. To find the LCM of 18 and 27.</p>

99 <p>The LCM of 18 and 27 is 54. To find the LCM of 18 and 27.</p>

101 <p>Multiples of 18 = 18,36,54,72;</p>

100 <p>Multiples of 18 = 18,36,54,72;</p>

102 <p>Multiples of 27= 27,54,81,108.</p>

101 <p>Multiples of 27= 27,54,81,108.</p>

103 <p>The LCM of 18 and 27 is 54.</p>

102 <p>The LCM of 18 and 27 is 54.</p>

104 <h3>2.There are how many factors in 3600?</h3>

103 <h3>2.There are how many factors in 3600?</h3>

105 <p>There are 45 factors of 3600, but the prime factors are 2,3,5. </p>

104 <p>There are 45 factors of 3600, but the prime factors are 2,3,5. </p>

106 <h3>3.Write the LCM of 15,18,24,27 and 56 ?</h3>

105 <h3>3.Write the LCM of 15,18,24,27 and 56 ?</h3>

107 <p>The LCM of 15,18,24,27 and 56 is 7560.</p>

106 <p>The LCM of 15,18,24,27 and 56 is 7560.</p>

108 <h3>4.What is the LCM of 8,14 and 9?</h3>

107 <h3>4.What is the LCM of 8,14 and 9?</h3>

109 <p> 8=23</p>

108 <p> 8=23</p>

110 <p>14=2x7</p>

109 <p>14=2x7</p>

111 <p>9=32</p>

110 <p>9=32</p>

112 <p>8x7x9=504 </p>

111 <p>8x7x9=504 </p>

113 <h3>5.If the LCM of two numbers a and b is 840, and one of the numbers is 28, find the smallest possible value of b?</h3>

112 <h3>5.If the LCM of two numbers a and b is 840, and one of the numbers is 28, find the smallest possible value of b?</h3>

114 <p>LCM(a, b)= a x b/GCD(a, b)</p>

113 <p>LCM(a, b)= a x b/GCD(a, b)</p>

115 <p>a=28 and LCM(a, b)=840</p>

114 <p>a=28 and LCM(a, b)=840</p>

116 <p>2x3x5=30. </p>

115 <p>2x3x5=30. </p>

117 <h2>Important glossaries on the LCM of 15 and 14</h2>

116 <h2>Important glossaries on the LCM of 15 and 14</h2>

118 <ul><li><strong>Prime Factor:</strong>A natural number or whole number which has factors that are 1 and itself. For Example, 3 is a prime number.</li>

117 <ul><li><strong>Prime Factor:</strong>A natural number or whole number which has factors that are 1 and itself. For Example, 3 is a prime number.</li>

119 </ul><ul><li><strong>Prime Factorization:</strong>The process of breaking down a number into its prime factors is called Prime Factorization. For example, the factorization of 14 is 2×7.</li>

118 </ul><ul><li><strong>Prime Factorization:</strong>The process of breaking down a number into its prime factors is called Prime Factorization. For example, the factorization of 14 is 2×7.</li>

120 </ul><ul><li><strong>Co-prime numbers:</strong>numbers which have the only positive divisor of them both as 1. For example, 6 and 7. </li>

119 </ul><ul><li><strong>Co-prime numbers:</strong>numbers which have the only positive divisor of them both as 1. For example, 6 and 7. </li>

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

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

122 <p>▶</p>

121 <p>▶</p>

123 <h2>Hiralee Lalitkumar Makwana</h2>

122 <h2>Hiralee Lalitkumar Makwana</h2>

124 <h3>About the Author</h3>

123 <h3>About the Author</h3>

125 <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>

124 <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>

126 <h3>Fun Fact</h3>

125 <h3>Fun Fact</h3>

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

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