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1 - <p>363 Learners</p>

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

3 <p>The smallest positive integer that divides the numbers with no numbers left behind is the LCM of 60 and 75. Did you know? We apply LCM unknowingly in everyday situations like setting alarms and to synchronize traffic lights and when making music. In this article, let’s now learn to find LCMs of 60 and 75.</p>

4 <h2>What is LCM of 60 and 75</h2>

5 <p>We can find the LCM using listing<a>multiples</a>method,<a>prime factorization</a>method and the<a>long division</a>method. These methods are explained here, apply a method that fits your understanding well. </p>

6 <h3>LCM of 60 and 75 using listing multiples method</h3>

7 <p><strong>Step 1:</strong>List the multiples<a>of</a>each of the<a>numbers</a>; </p>

8 <p>60 = 60,120,180,240,300,… </p>

9 <p>75= 75,150,225,300,…</p>

10 <p><strong>Step 2:</strong>Find the smallest number in both the lists </p>

11 <p>LCM (60,75) = 300 </p>

12 <h3>LCM of 60 and 75 using prime factorization method</h3>

13 <p><strong>Step 1:</strong>Prime factorize the numbers</p>

14 <p> 60 = 2×2×3×5</p>

15 <p>75 = 3×5×5 </p>

16 <p><strong>Step 2:</strong>find highest<a>powers</a></p>

17 <p>22,3 and 52 </p>

18 <p><strong>Step 3:</strong>Multiply the highest powers of the numbers</p>

19 <p>22×3×52 = 300 </p>

20 <p>LCM(60,75) = 300 </p>

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23 <h3>LCM of 60 and 75 using division method</h3>

22 <h3>LCM of 60 and 75 using division method</h3>

24 <ul><li>Write the numbers in a row </li>

23 <ul><li>Write the numbers in a row </li>

25 </ul><ul><li>Divide them with a common prime<a>factor</a></li>

24 </ul><ul><li>Divide them with a common prime<a>factor</a></li>

26 </ul><ul><li>Carry forward numbers that are left undivided </li>

25 </ul><ul><li>Carry forward numbers that are left undivided </li>

27 </ul><ul><li>Continue dividing until the<a>remainder</a>is ‘1’ </li>

26 </ul><ul><li>Continue dividing until the<a>remainder</a>is ‘1’ </li>

28 </ul><ul><li>Multiply the divisors to find the LCM</li>

27 </ul><ul><li>Multiply the divisors to find the LCM</li>

29 </ul><ul><li>LCM (60,75) = 300 </li>

28 </ul><ul><li>LCM (60,75) = 300 </li>

30 </ul><h2>Common mistakes and how to avoid them while finding the LCM of 60 and 75</h2>

29 </ul><h2>Common mistakes and how to avoid them while finding the LCM of 60 and 75</h2>

31 <p>Listed here are a few mistakes children may make when trying to find the LCM due to confusion or due to unclear understanding. Be mindful, understand, learn and avoid! </p>

30 <p>Listed here are a few mistakes children may make when trying to find the LCM due to confusion or due to unclear understanding. Be mindful, understand, learn and avoid! </p>

32 <h3>Problem 1</h3>

31 <h3>Problem 1</h3>

33 <p>Verify that the relationship between GCD and LCM holds true for 60 and 75: LCM(a, b)×GCD(a, b)=a×b</p>

32 <p>Verify that the relationship between GCD and LCM holds true for 60 and 75: LCM(a, b)×GCD(a, b)=a×b</p>

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

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

35 <p>GCD(60, 75) = 15</p>

34 <p>GCD(60, 75) = 15</p>

36 <p>LCM(60, 75) = 300</p>

35 <p>LCM(60, 75) = 300</p>

37 <p>LCM (60,75)×GCD(60,75) = 300×15 = 4500</p>

36 <p>LCM (60,75)×GCD(60,75) = 300×15 = 4500</p>

38 <p>60×75 = 4500 </p>

37 <p>60×75 = 4500 </p>

39 <h3>Explanation</h3>

38 <h3>Explanation</h3>

40 <p>The formula holds because the product of the LCM and GCD equals the product of the original numbers. </p>

39 <p>The formula holds because the product of the LCM and GCD equals the product of the original numbers. </p>

41 <p>Well explained 👍</p>

40 <p>Well explained 👍</p>

42 <h3>Problem 2</h3>

41 <h3>Problem 2</h3>

43 <p>What percentage of the product of 60 and 75 is their LCM?</p>

42 <p>What percentage of the product of 60 and 75 is their LCM?</p>

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

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

45 <p>Product of 60 and 75 = 60 × 75 = 4500</p>

44 <p>Product of 60 and 75 = 60 × 75 = 4500</p>

46 <p>LCM = 300</p>

45 <p>LCM = 300</p>

47 <p>Percentage = 300/4500×100 = 6.67% </p>

46 <p>Percentage = 300/4500×100 = 6.67% </p>

48 <h3>Explanation</h3>

47 <h3>Explanation</h3>

49 <p> The LCM is 6.67% of the product of the two numbers.</p>

48 <p> The LCM is 6.67% of the product of the two numbers.</p>

50 <p>Well explained 👍</p>

49 <p>Well explained 👍</p>

51 <h3>Problem 3</h3>

50 <h3>Problem 3</h3>

52 <p>If the LCM of 60 and a missing number xxx is 300, what is xxx?</p>

51 <p>If the LCM of 60 and a missing number xxx is 300, what is xxx?</p>

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

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

54 <p>LCM(60,x) = 300</p>

53 <p>LCM(60,x) = 300</p>

55 <p>Prime factorization of 60 = 2² × 3 × 5</p>

54 <p>Prime factorization of 60 = 2² × 3 × 5</p>

56 <p>Since 300 = 2² × 3 × 5²,</p>

55 <p>Since 300 = 2² × 3 × 5²,</p>

57 <p>the missing number x must provide the extra factor of 5.</p>

56 <p>the missing number x must provide the extra factor of 5.</p>

58 <p>Thus, x=75 </p>

57 <p>Thus, x=75 </p>

59 <h3>Explanation</h3>

58 <h3>Explanation</h3>

60 <p>The missing number x is the number that would provide the required factors to make the LCM 300.</p>

59 <p>The missing number x is the number that would provide the required factors to make the LCM 300.</p>

61 <p>Well explained 👍</p>

60 <p>Well explained 👍</p>

62 <h3>Problem 4</h3>

61 <h3>Problem 4</h3>

63 <p>Is 600 a common multiple of 60 and 75?</p>

62 <p>Is 600 a common multiple of 60 and 75?</p>

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

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

65 <p>600/60 = 10</p>

64 <p>600/60 = 10</p>

66 <p>600/75 = 8 </p>

65 <p>600/75 = 8 </p>

67 <h3>Explanation</h3>

66 <h3>Explanation</h3>

68 <p>Since 600 is divisible by both 60 and 75, it is a common multiple. However, it is not the least common multiple, as the LCM is 300. </p>

67 <p>Since 600 is divisible by both 60 and 75, it is a common multiple. However, it is not the least common multiple, as the LCM is 300. </p>

69 <p>Well explained 👍</p>

68 <p>Well explained 👍</p>

70 <h2>FAQs on the LCM of 60 and 75</h2>

69 <h2>FAQs on the LCM of 60 and 75</h2>

71 <h3>1. Find the GCF of 60 and 75 and list all the factors of the numbers.</h3>

70 <h3>1. Find the GCF of 60 and 75 and list all the factors of the numbers.</h3>

72 <p>Factors of;</p>

71 <p>Factors of;</p>

73 <p>60-1,2,3,4,5,6,10,12,15,20,30,60</p>

72 <p>60-1,2,3,4,5,6,10,12,15,20,30,60</p>

74 <p>75-1,3,5,15,25,75</p>

73 <p>75-1,3,5,15,25,75</p>

75 <p>GCF(60,75) = 15 </p>

74 <p>GCF(60,75) = 15 </p>

76 <h3>2.Find the LCM of 60,75 and 90.</h3>

75 <h3>2.Find the LCM of 60,75 and 90.</h3>

77 <p>Prime factorization of the numbers 60,75 and 90; </p>

76 <p>Prime factorization of the numbers 60,75 and 90; </p>

78 <p>60 = 2×2×3×5</p>

77 <p>60 = 2×2×3×5</p>

79 <p>75 = 3×5×5</p>

78 <p>75 = 3×5×5</p>

80 <p>90= 3×3×2×5 </p>

79 <p>90= 3×3×2×5 </p>

81 <p>LCM (60,75,90) = 900 </p>

80 <p>LCM (60,75,90) = 900 </p>

82 <h3>3.Find the LCM of 30,60 and 75?</h3>

81 <h3>3.Find the LCM of 30,60 and 75?</h3>

83 <p>Prime factorization of the numbers 30,60 and75;</p>

82 <p>Prime factorization of the numbers 30,60 and75;</p>

84 <p>30 =2×3×5</p>

83 <p>30 =2×3×5</p>

85 <p>60 = 2×2×3×5</p>

84 <p>60 = 2×2×3×5</p>

86 <p>75 = 3×5×5</p>

85 <p>75 = 3×5×5</p>

87 <p>LCM (30,60,75) = 300 </p>

86 <p>LCM (30,60,75) = 300 </p>

88 <h3>4.Find the LCM of 50,60 and 75?</h3>

87 <h3>4.Find the LCM of 50,60 and 75?</h3>

89 <p>Prime factorization of the numbers; </p>

88 <p>Prime factorization of the numbers; </p>

90 <p>50 = 2×5×5</p>

89 <p>50 = 2×5×5</p>

91 <p>60 = 2×2×3×5</p>

90 <p>60 = 2×2×3×5</p>

92 <p>75 = 3×5×5</p>

91 <p>75 = 3×5×5</p>

93 <p>LCM (50,30,60) = 300 </p>

92 <p>LCM (50,30,60) = 300 </p>

94 <h3>5. Find the LCM of 60,75 and 105?</h3>

93 <h3>5. Find the LCM of 60,75 and 105?</h3>

95 <p>Write down the multiples of the numbers </p>

94 <p>Write down the multiples of the numbers </p>

96 <p>60 = 60,120,180,240,30,…2100</p>

95 <p>60 = 60,120,180,240,30,…2100</p>

97 <p>75 = 75,150,225,300,….2100</p>

96 <p>75 = 75,150,225,300,….2100</p>

98 <p>105 = 105,210,315,420,…2100</p>

97 <p>105 = 105,210,315,420,…2100</p>

99 <p>LCM (60,75,105) = 2100 </p>

98 <p>LCM (60,75,105) = 2100 </p>

100 <h2>Important glossaries for LCM of 60 and 75</h2>

99 <h2>Important glossaries for LCM of 60 and 75</h2>

101 <ul><li><strong>Multiple:</strong>the result after multiplication of a number and an integer. To explain, 75×5 =375; 375 is a multiple of 75. </li>

100 <ul><li><strong>Multiple:</strong>the result after multiplication of a number and an integer. To explain, 75×5 =375; 375 is a multiple of 75. </li>

102 </ul><ul><li><strong>Prime Factor:</strong>A number with only two factors, 1 and the number. For example,7, its factors are only 1 and 7 and the number when divided by any other integer will leave a remainder behind. </li>

101 </ul><ul><li><strong>Prime Factor:</strong>A number with only two factors, 1 and the number. For example,7, its factors are only 1 and 7 and the number when divided by any other integer will leave a remainder behind. </li>

103 </ul><ul><li><strong>Prime Factorization:</strong>breaking a number down into its prime factors. For example, 60 is written as the product of 2×2×3×5. </li>

102 </ul><ul><li><strong>Prime Factorization:</strong>breaking a number down into its prime factors. For example, 60 is written as the product of 2×2×3×5. </li>

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

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

105 <p>▶</p>

104 <p>▶</p>

106 <h2>Hiralee Lalitkumar Makwana</h2>

105 <h2>Hiralee Lalitkumar Makwana</h2>

107 <h3>About the Author</h3>

106 <h3>About the Author</h3>

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>

107 <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>

109 <h3>Fun Fact</h3>

108 <h3>Fun Fact</h3>

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

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