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

3 <p>By ascertaining the LCM of the numbers we can simplify the arithmetic operations with fractions by equating the denominators and in other mathematical scenarios. The smallest positive integer and a multiple of both 24 and 30, is the LCM of the numbers.</p>

4 <h2>What is the LCM of 24 and 32?</h2>

5 <h2>How to Find the LCM of 24 and 32?</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 24 and 32 using the Listing Multiples Method</h3>

8 <p>The LCM of 24 and 32 can be calculated using the following steps:</p>

9 <p>Step1:Write down the multiples of each number</p>

10 <p>Multiples of 24 =24,48,72,96,144,…</p>

11 <p>Multiples of 32 = 32,64,96,…</p>

12 <p>Step1: Ascertain the smallest multiple from the listed multiples:</p>

13 <p>The smallest<a>common multiple</a>is 96.</p>

14 <p>Thus, LCM(24,32) = 96</p>

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17 <h3>LCM of 24 and 32 using the Prime Factorization Method</h3>

16 <h3>LCM of 24 and 32 using the Prime Factorization Method</h3>

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>

17 <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>

19 <p><strong>Step1:</strong>Find the prime factors of each number:</p>

18 <p><strong>Step1:</strong>Find the prime factors of each number:</p>

20 <p>32 = 2×2×2×2×2 </p>

19 <p>32 = 2×2×2×2×2 </p>

21 <p>24 = 2×2×2×3 </p>

20 <p>24 = 2×2×2×3 </p>

22 <p><strong>Step2:</strong> Take the highest powers of each prime factor and multiply the highest powers to get the LCM:</p>

21 <p><strong>Step2:</strong> Take the highest powers of each prime factor and multiply the highest powers to get the LCM:</p>

23 <p>LCM(32,24) = 96</p>

22 <p>LCM(32,24) = 96</p>

24 <h3>LCM of 24 and 32 using the Division Method</h3>

23 <h3>LCM of 24 and 32 using the Division Method</h3>

25 <p>In the division method we, divide the numbers by their common prime factors and multiplying the divisors to find the LCM.</p>

24 <p>In the division method we, divide the numbers by their common prime factors and multiplying the divisors to find the LCM.</p>

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

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

27 <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. 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>

26 <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. 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>

28 <p><strong>Step 3:</strong>The LCM of the numbers is the<a>product</a>of the prime numbers in the first column,<a>i</a>.e, </p>

27 <p><strong>Step 3:</strong>The LCM of the numbers is the<a>product</a>of the prime numbers in the first column,<a>i</a>.e, </p>

29 <p>Thus, LCM(32,24) = 96</p>

28 <p>Thus, LCM(32,24) = 96</p>

30 <h2>Common Mistakes and how to avoid them in LCM of 24 and 32</h2>

29 <h2>Common Mistakes and how to avoid them in LCM of 24 and 32</h2>

31 <p>Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 24 and 32 make a note while practicing.</p>

30 <p>Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 24 and 32 make a note while practicing.</p>

32 <h3>Problem 1</h3>

31 <h3>Problem 1</h3>

33 <p>a=24, b=32. Express the LCM of the numbers a and b as a function of the prime factorization of the digits. Prove that the method used works universally for any pair of integers.</p>

32 <p>a=24, b=32. Express the LCM of the numbers a and b as a function of the prime factorization of the digits. Prove that the method used works universally for any pair of integers.</p>

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

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

35 <p>The prime factorization of a and b; </p>

34 <p>The prime factorization of a and b; </p>

36 <p>a = 23×31</p>

35 <p>a = 23×31</p>

37 <p>b = 25</p>

36 <p>b = 25</p>

38 <p>Pick the maximum powers of the primes; </p>

37 <p>Pick the maximum powers of the primes; </p>

39 <p>LCM(a,b) = 25×31</p>

38 <p>LCM(a,b) = 25×31</p>

40 <p>LCM = 96, using prime factorization. </p>

39 <p>LCM = 96, using prime factorization. </p>

41 <h3>Explanation</h3>

40 <h3>Explanation</h3>

42 <p>The LCM of any two numbers is the smallest number that is divisible by them both. When we prime factorize, we make sure that all the factors are accounted for and the highest power of each prime is selected. By doing so, we ensure that the resultant number is divisible by both a and b. This method works universally, for all/any two given numbers as it is based on the principle that divisibility is to be ensured by combining prime factors in their highest powers. </p>

41 <p>The LCM of any two numbers is the smallest number that is divisible by them both. When we prime factorize, we make sure that all the factors are accounted for and the highest power of each prime is selected. By doing so, we ensure that the resultant number is divisible by both a and b. This method works universally, for all/any two given numbers as it is based on the principle that divisibility is to be ensured by combining prime factors in their highest powers. </p>

43 <p>Well explained 👍</p>

42 <p>Well explained 👍</p>

44 <h3>Problem 2</h3>

43 <h3>Problem 2</h3>

45 <p>Traffic light A changes every 32 minutes and traffic light B switches every 24 minutes. When will they next turn green simultaneously.</p>

44 <p>Traffic light A changes every 32 minutes and traffic light B switches every 24 minutes. When will they next turn green simultaneously.</p>

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

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

47 <p>We use the formula; </p>

46 <p>We use the formula; </p>

48 <p>LCM(a, b) = a×b/HCF(a, b) where, a=32, b=24</p>

47 <p>LCM(a, b) = a×b/HCF(a, b) where, a=32, b=24</p>

49 <p>HCF of 24 and 32; </p>

48 <p>HCF of 24 and 32; </p>

50 <p>Factors of 32 = 1,2,4,8,16,32</p>

49 <p>Factors of 32 = 1,2,4,8,16,32</p>

51 <p>Factors of 24 = 1,2,3,4,6,8,12,24</p>

50 <p>Factors of 24 = 1,2,3,4,6,8,12,24</p>

52 <p>HCF(32,24)= 8 </p>

51 <p>HCF(32,24)= 8 </p>

53 <p>Applying the ascertained HCF in the formula; </p>

52 <p>Applying the ascertained HCF in the formula; </p>

54 <p>LCM(a, b) = a×b/HCF(a, b) </p>

53 <p>LCM(a, b) = a×b/HCF(a, b) </p>

55 <p>LCM(32,24) = 32×24/8 = 96 </p>

54 <p>LCM(32,24) = 32×24/8 = 96 </p>

56 <p>LCM(32,24) = 96 </p>

55 <p>LCM(32,24) = 96 </p>

57 <h3>Explanation</h3>

56 <h3>Explanation</h3>

58 <p> The traffic lights will change simultaneously in 96 minutes. </p>

57 <p> The traffic lights will change simultaneously in 96 minutes. </p>

59 <p>Well explained 👍</p>

58 <p>Well explained 👍</p>

60 <h3>Problem 3</h3>

59 <h3>Problem 3</h3>

61 <p>LCM of 24x and 32x2 is 96xn. Find n.</p>

60 <p>LCM of 24x and 32x2 is 96xn. Find n.</p>

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

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

63 <p>First, we find the LCM of 24 and 32 (numerical coefficients) </p>

62 <p>First, we find the LCM of 24 and 32 (numerical coefficients) </p>

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

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

65 <p>32 = 2×2×2×2×2 </p>

64 <p>32 = 2×2×2×2×2 </p>

66 <p>24= 2×2×2×3 </p>

65 <p>24= 2×2×2×3 </p>

67 <p>LCM(24,32) = 96</p>

66 <p>LCM(24,32) = 96</p>

68 <p>For variables x and x2, the highest power of x is taken by the LCM, therefore we take x2. </p>

67 <p>For variables x and x2, the highest power of x is taken by the LCM, therefore we take x2. </p>

69 <p>I.e., LCM (24x,32x2) = 96x2</p>

68 <p>I.e., LCM (24x,32x2) = 96x2</p>

70 <p>By comparing 96xn, we have </p>

69 <p>By comparing 96xn, we have </p>

71 <p>xn=x2</p>

70 <p>xn=x2</p>

72 <p>n= 2 </p>

71 <p>n= 2 </p>

73 <h3>Explanation</h3>

72 <h3>Explanation</h3>

74 <p>By taking the highest power of each variable involved, we find the LCM of the variable powers. n=2. </p>

73 <p>By taking the highest power of each variable involved, we find the LCM of the variable powers. n=2. </p>

75 <p>Well explained 👍</p>

74 <p>Well explained 👍</p>

76 <h2>FAQs on LCM of 24 and 32</h2>

75 <h2>FAQs on LCM of 24 and 32</h2>

77 <h3>1.What is the HCF of 24 and 32?</h3>

76 <h3>1.What is the HCF of 24 and 32?</h3>

78 <p>Factors of 32= 1,2,4,8,16,32 </p>

77 <p>Factors of 32= 1,2,4,8,16,32 </p>

79 <p>Factors of 24 = 1,2,3,4,6,8,12,24,24 </p>

78 <p>Factors of 24 = 1,2,3,4,6,8,12,24,24 </p>

80 <p>HCF (32,24) = 8 </p>

79 <p>HCF (32,24) = 8 </p>

81 <h3>2.What is the LCM of 36 and 24?</h3>

80 <h3>2.What is the LCM of 36 and 24?</h3>

82 <p>Prime factorization of 36 → 3×2×2×3</p>

81 <p>Prime factorization of 36 → 3×2×2×3</p>

83 <p>Prime factorization of 24 →2×2×2×2×3</p>

82 <p>Prime factorization of 24 →2×2×2×2×3</p>

84 <p>LCM(36,24) = 144 </p>

83 <p>LCM(36,24) = 144 </p>

85 <h3>3.What is the LCM of 32 and 40?</h3>

84 <h3>3.What is the LCM of 32 and 40?</h3>

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

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

87 <p> 32 = 2×2×2×2×2</p>

86 <p> 32 = 2×2×2×2×2</p>

88 <p> 40 = 2×2×2×5 </p>

87 <p> 40 = 2×2×2×5 </p>

89 <p>LCM (32,40) = 160 </p>

88 <p>LCM (32,40) = 160 </p>

90 <h3>4.What is the LCM of 8, 32 and 24?</h3>

89 <h3>4.What is the LCM of 8, 32 and 24?</h3>

91 <p>Prime factorize 8,32 and 24; </p>

90 <p>Prime factorize 8,32 and 24; </p>

92 <p>32 = 2×2×2×2×2</p>

91 <p>32 = 2×2×2×2×2</p>

93 <p>8 = 2×2×2</p>

92 <p>8 = 2×2×2</p>

94 <p>40 = 2×2×2×5 </p>

93 <p>40 = 2×2×2×5 </p>

95 <p>LCM (8,32,40) = 96 </p>

94 <p>LCM (8,32,40) = 96 </p>

96 <h3>5.What is the LCM of 32,24 and 72?</h3>

95 <h3>5.What is the LCM of 32,24 and 72?</h3>

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

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

98 <p>32 = 2×2×2×2×2</p>

97 <p>32 = 2×2×2×2×2</p>

99 <p>24 = 2×2×2×2×3</p>

98 <p>24 = 2×2×2×2×3</p>

100 <p>72 = 3×2×2×3×2</p>

99 <p>72 = 3×2×2×3×2</p>

101 <p>LCM (32,24,72) = 288 </p>

100 <p>LCM (32,24,72) = 288 </p>

102 <h2>Important glossaries for the LCM of 24 and 32</h2>

101 <h2>Important glossaries for the LCM of 24 and 32</h2>

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

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

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

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

105 </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>

104 </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>

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

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

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

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

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

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

109 <p>▶</p>

108 <p>▶</p>

110 <h2>Hiralee Lalitkumar Makwana</h2>

109 <h2>Hiralee Lalitkumar Makwana</h2>

111 <h3>About the Author</h3>

110 <h3>About the Author</h3>

112 <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>

111 <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 <h3>Fun Fact</h3>

112 <h3>Fun Fact</h3>

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

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