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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 24 and 30. 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 24 and 30?</h2>

5 <h2>How to find the LCM of 24 and 30 ?</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 30 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 24 = 24,48,…,120,…</p>

11 <p>Multiples of 30 = 30,…,120,…</p>

12 <p><strong>Step 2.</strong>Ascertain the smallest multiple from the listed multiples of 24 and 30. </p>

13 <p>The LCM (The Least common multiple) of 24 and 30 is 24. I.e., 120 is divisible by 24 and 30 with no reminder. </p>

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16 <h3>LCM of 24 and 30 using the Prime Factorization</h3>

15 <h3>LCM of 24 and 30 using the Prime Factorization</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>Step1: Find the prime factors of the numbers:</p>

17 <p>Step1: Find the prime factors of the numbers:</p>

19 <p>Prime factorization of 24 = 2×2×2×3</p>

18 <p>Prime factorization of 24 = 2×2×2×3</p>

20 <p>Prime factorization of 30 = 2×3×5 </p>

19 <p>Prime factorization of 30 = 2×3×5 </p>

21 <p> <strong>Step 2:</strong>Take the highest power of each prime factor:</p>

20 <p> <strong>Step 2:</strong>Take the highest power of each prime factor:</p>

22 <p>- 2,2,2,3,5</p>

21 <p>- 2,2,2,3,5</p>

23 <p><strong>Step 3:</strong>Multiply the ascertained factors to get the LCM: </p>

22 <p><strong>Step 3:</strong>Multiply the ascertained factors to get the LCM: </p>

24 <p>LCM (8,12) = 2×2×2×3×5 = 120 </p>

23 <p>LCM (8,12) = 2×2×2×3×5 = 120 </p>

25 <h3>LCM of 24 and 30 using the Division Method</h3>

24 <h3>LCM of 24 and 30 using the Division Method</h3>

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

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

27 <p><strong>Step 1</strong>: Write down the numbers in a row;</p>

26 <p><strong>Step 1</strong>: Write down the numbers in a row;</p>

28 <p><strong>Step 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 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>

29 <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 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>

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

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

31 <p>2×2×2×3×5 = 120 </p>

30 <p>2×2×2×3×5 = 120 </p>

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

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

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

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

34 <h3>Problem 1</h3>

33 <h3>Problem 1</h3>

35 <p>Trains Y and X arrive every 8 minutes and 12 minutes at the station at the same time. In how long will they arrive together again?</p>

34 <p>Trains Y and X arrive every 8 minutes and 12 minutes at the station at the same time. In how long will they arrive together again?</p>

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

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

37 <p>The LCM of 24 and 30 = 120 </p>

36 <p>The LCM of 24 and 30 = 120 </p>

38 <h3>Explanation</h3>

37 <h3>Explanation</h3>

39 <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 120 minutes. </p>

38 <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 120 minutes. </p>

40 <p>Well explained 👍</p>

39 <p>Well explained 👍</p>

41 <h3>Problem 2</h3>

40 <h3>Problem 2</h3>

42 <p>In a factory, machine A finishes a cycle every 24 minutes, machine B finishes a cycle in 30 minutes. Using the LCM formula, ascertain when will they complete a cycle simultaneously?</p>

41 <p>In a factory, machine A finishes a cycle every 24 minutes, machine B finishes a cycle in 30 minutes. Using the LCM formula, ascertain when will they complete a cycle simultaneously?</p>

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

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

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

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

45 <p>LCM(a, b) = a×b/HCF(a, b) where, a=24, b=30</p>

44 <p>LCM(a, b) = a×b/HCF(a, b) where, a=24, b=30</p>

46 <p>HCF of 24 and 30; </p>

45 <p>HCF of 24 and 30; </p>

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

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

48 <p>Factors of 30 = 1,2,3,5,6,10,15,30 </p>

47 <p>Factors of 30 = 1,2,3,5,6,10,15,30 </p>

49 <p>HCF (24,30)= 6 </p>

48 <p>HCF (24,30)= 6 </p>

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

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

51 <p>LCM(a, b) = a×b/HCF(a, b) </p>

50 <p>LCM(a, b) = a×b/HCF(a, b) </p>

52 <p>LCM(24,30) = 24×30/6 = 120 </p>

51 <p>LCM(24,30) = 24×30/6 = 120 </p>

53 <p>LCM(24,30) = 120 </p>

52 <p>LCM(24,30) = 120 </p>

54 <h3>Explanation</h3>

53 <h3>Explanation</h3>

55 <p>Machines A and B will complete their cycle together every 120 minutes. </p>

54 <p>Machines A and B will complete their cycle together every 120 minutes. </p>

56 <p>Well explained 👍</p>

55 <p>Well explained 👍</p>

57 <h3>Problem 3</h3>

56 <h3>Problem 3</h3>

58 <p>Student A finishes his work in 24 minutes and student B finishes his work in 30 minutes. If A and B start working together, after how long will they complete the task?</p>

57 <p>Student A finishes his work in 24 minutes and student B finishes his work in 30 minutes. If A and B start working together, after how long will they complete the task?</p>

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

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

60 <p>To begin, calculate the work rates of student A and B; </p>

59 <p>To begin, calculate the work rates of student A and B; </p>

61 <p>Student A = 1/24 </p>

60 <p>Student A = 1/24 </p>

62 <p>Student B = 1/30 </p>

61 <p>Student B = 1/30 </p>

63 <p>Combined work rate; </p>

62 <p>Combined work rate; </p>

64 <p>1/24+1/30 </p>

63 <p>1/24+1/30 </p>

65 <p>To add the fractions, equate the denominators by finding their LCM </p>

64 <p>To add the fractions, equate the denominators by finding their LCM </p>

66 <p>Prime factorization of 24 = 2×2×2×3</p>

65 <p>Prime factorization of 24 = 2×2×2×3</p>

67 <p>Prime factorization of 30 = 2×3×5 </p>

66 <p>Prime factorization of 30 = 2×3×5 </p>

68 <p>LCM of 24, 30 = 120</p>

67 <p>LCM of 24, 30 = 120</p>

69 <p>1/24 ×5/5 = 5/120</p>

68 <p>1/24 ×5/5 = 5/120</p>

70 <p>1/30×4/4 = 4/120</p>

69 <p>1/30×4/4 = 4/120</p>

71 <p>Combined work rate = 5/120+4/120 = 9/120 = 13.33 minutes </p>

70 <p>Combined work rate = 5/120+4/120 = 9/120 = 13.33 minutes </p>

72 <h3>Explanation</h3>

71 <h3>Explanation</h3>

73 <p>Students A and B will complete their task in approximately 13.33 minutes if they work together. </p>

72 <p>Students A and B will complete their task in approximately 13.33 minutes if they work together. </p>

74 <p>Well explained 👍</p>

73 <p>Well explained 👍</p>

75 <h2>FAQ’s on LCM of 24 and 30</h2>

74 <h2>FAQ’s on LCM of 24 and 30</h2>

76 <h3>1.What is the HCF of 24 and 30?</h3>

75 <h3>1.What is the HCF of 24 and 30?</h3>

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

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

78 <p>Factors of 30 = 1,2,3,5,6,10,15,30 </p>

77 <p>Factors of 30 = 1,2,3,5,6,10,15,30 </p>

79 <p>HCF(24,30) = 6 </p>

78 <p>HCF(24,30) = 6 </p>

80 <h3>2. List the factors of 24 and 30.</h3>

79 <h3>2. List the factors of 24 and 30.</h3>

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

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

82 <p>Factors of 30 = 1,2,3,5,6,10,15,30 </p>

81 <p>Factors of 30 = 1,2,3,5,6,10,15,30 </p>

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

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

84 <h3>3.What is the LCM of 25 and 30?</h3>

83 <h3>3.What is the LCM of 25 and 30?</h3>

85 <p>Prime factorization of 25 = 5×5</p>

84 <p>Prime factorization of 25 = 5×5</p>

86 <p> Prime factorization of 30 = 2×3×5 </p>

85 <p> Prime factorization of 30 = 2×3×5 </p>

87 <p>LCM (25,30)= 5×5×2×3 = 150 </p>

86 <p>LCM (25,30)= 5×5×2×3 = 150 </p>

88 <h3>4.What is the LCM of 20 and 30?</h3>

87 <h3>4.What is the LCM of 20 and 30?</h3>

89 <p>Prime factorization of 20 = 2×2×5 </p>

88 <p>Prime factorization of 20 = 2×2×5 </p>

90 <p>Prime factorization of 30 = 2×3×5 </p>

89 <p>Prime factorization of 30 = 2×3×5 </p>

91 <p>LCM (20,30) = 2×2×3×5 = 60 </p>

90 <p>LCM (20,30) = 2×2×3×5 = 60 </p>

92 <h3>5. List the prime factors of 30.</h3>

91 <h3>5. List the prime factors of 30.</h3>

93 <p>Factors of 30-1,2,3,5,6,10,15,30 </p>

92 <p>Factors of 30-1,2,3,5,6,10,15,30 </p>

94 <h2>Important glossaries for LCM of 24 and 30</h2>

93 <h2>Important glossaries for LCM of 24 and 30</h2>

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

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

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

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

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

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

98 </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>

97 </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>

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

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

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

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

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

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

102 <p>▶</p>

101 <p>▶</p>

103 <h2>Hiralee Lalitkumar Makwana</h2>

102 <h2>Hiralee Lalitkumar Makwana</h2>

104 <h3>About the Author</h3>

103 <h3>About the Author</h3>

105 <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>

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>

106 <h3>Fun Fact</h3>

105 <h3>Fun Fact</h3>

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

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