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

3 <p>LCM is the smallest number divisible by 3, 5 and 10. LCM helps to solve problems with fractions, and scenarios like managing supplies and restocking. In this article, we will learn how to find LCM of 3, 5 and 10 by using different methods.</p>

4 <h2>What is the LCM of 3, 5 and 10?</h2>

5 <h2>How to find the LCM of 3, 5 and 10?</h2>

6 <p>There are various methods to find the LCM. The methods to find the LCM are:</p>

7 <ul><li>Listing method</li>

8 </ul><ul><li>Prime factorization method </li>

9 </ul><ul><li>Division method </li>

10 </ul><h3>LCM of 3, 5 and 10 using the Listing Method</h3>

11 <p>In the listing method, we write a multiple of the numbers first and then find the smallest<a>common multiple</a>.</p>

12 <p><strong>Step 1:</strong>Identify the multiples of 3, 5 and 10</p>

13 <p>Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33….</p>

14 <p>Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50….</p>

15 <p>Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90….</p>

16 <p><strong>Step 2:</strong>Ascertain the smallest multiple from the listed multiples of 3, 5 and 10</p>

17 <p>The LCM of 3, 5 and 10 is 30 </p>

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20 <h3>LCM of 3, 5 and 10 using the Prime Factorization Method</h3>

19 <h3>LCM of 3, 5 and 10 using the Prime Factorization Method</h3>

21 <p>The<a>prime 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>

20 <p>The<a>prime 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>

22 <p><strong>Step 1:</strong>Find the prime factors of 3, 5 and 10</p>

21 <p><strong>Step 1:</strong>Find the prime factors of 3, 5 and 10</p>

23 <p>Prime factorization of 3: 31</p>

22 <p>Prime factorization of 3: 31</p>

24 <p>Prime factorization of 5: 51</p>

23 <p>Prime factorization of 5: 51</p>

25 <p>Prime factorization of 10: 21 × 51</p>

24 <p>Prime factorization of 10: 21 × 51</p>

26 <p><strong>Step 2:</strong>Multiply the highest power of each factor ascertained to get the LCM </p>

25 <p><strong>Step 2:</strong>Multiply the highest power of each factor ascertained to get the LCM </p>

27 <p>LCM of 3, 5 and 10 = 21 × 31 × 51 = 30</p>

26 <p>LCM of 3, 5 and 10 = 21 × 31 × 51 = 30</p>

28 <h3>LCM of 3, 5 and 10 using the Division Method</h3>

27 <h3>LCM of 3, 5 and 10 using the Division Method</h3>

29 <p>This method involves simultaneously dividing the numbers by their prime<a>factors</a>until they become 1 and multiplying the divisors to get the LCM. </p>

28 <p>This method involves simultaneously dividing the numbers by their prime<a>factors</a>until they become 1 and multiplying the divisors to get the LCM. </p>

30 <p><strong>Step 1:</strong>Write the numbers in a row, like 3, 5, 10.</p>

29 <p><strong>Step 1:</strong>Write the numbers in a row, like 3, 5, 10.</p>

31 <p><strong>Step 2:</strong>Start dividing the numbers with prime factors by 2 </p>

30 <p><strong>Step 2:</strong>Start dividing the numbers with prime factors by 2 </p>

32 <p>From the numbers 3, 5 and 10, only 10 is divisible by 2 (10 ÷ 2) which gives 5 as the<a>quotient</a>.</p>

31 <p>From the numbers 3, 5 and 10, only 10 is divisible by 2 (10 ÷ 2) which gives 5 as the<a>quotient</a>.</p>

33 <p>Now the numbers in the row will be 3, 5, 5</p>

32 <p>Now the numbers in the row will be 3, 5, 5</p>

34 <p><strong>Step 3:</strong>Move on to the next<a>prime number</a>, 3</p>

33 <p><strong>Step 3:</strong>Move on to the next<a>prime number</a>, 3</p>

35 <p>From the list 3, 5 and 5, only 3 is divisible by 3 (3 ÷ 3) which gives 1 as the quotient.</p>

34 <p>From the list 3, 5 and 5, only 3 is divisible by 3 (3 ÷ 3) which gives 1 as the quotient.</p>

36 <p>Now the numbers in the row will look like 1, 5, 5.</p>

35 <p>Now the numbers in the row will look like 1, 5, 5.</p>

37 <p><strong>Step 4:</strong>Move on to the next prime number 5.</p>

36 <p><strong>Step 4:</strong>Move on to the next prime number 5.</p>

38 <p> From the list 1, 5 and 5, only 5 is divisible by 5 (5 ÷ 5) which gives 1 as the quotient.</p>

37 <p> From the list 1, 5 and 5, only 5 is divisible by 5 (5 ÷ 5) which gives 1 as the quotient.</p>

39 <p>Now the numbers in the row will look like 1, 1, 1.</p>

38 <p>Now the numbers in the row will look like 1, 1, 1.</p>

40 <p><strong>Step 5</strong>: To find the LCM, multiply all the divisors used </p>

39 <p><strong>Step 5</strong>: To find the LCM, multiply all the divisors used </p>

41 <p>The divisors used are 2, 3 and 5. The<a>product</a>of 2, 3 and 5 is 30 (2×3×5 = 30)</p>

40 <p>The divisors used are 2, 3 and 5. The<a>product</a>of 2, 3 and 5 is 30 (2×3×5 = 30)</p>

42 <h2>Common Mistakes and how to avoid them while finding the LCM of 3, 5 and 10</h2>

41 <h2>Common Mistakes and how to avoid them while finding the LCM of 3, 5 and 10</h2>

43 <p>Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 3, 5 and 10 make a note while practicing. </p>

42 <p>Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 3, 5 and 10 make a note while practicing. </p>

44 <h3>Problem 1</h3>

43 <h3>Problem 1</h3>

45 <p>Can you tell whether the LCM of 3, 5 and 10 is 30? Also find the GCF of 3, 5 and 10</p>

44 <p>Can you tell whether the LCM of 3, 5 and 10 is 30? Also find the GCF of 3, 5 and 10</p>

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

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

47 <p>Yes, the LCM is 30. The GCF of 3, 5 and 10 is 1. </p>

46 <p>Yes, the LCM is 30. The GCF of 3, 5 and 10 is 1. </p>

48 <h3>Explanation</h3>

47 <h3>Explanation</h3>

49 <p>We can find the LCM of 30 by listing the multiples of 3, 5 and 10, and finding the least common multiple.</p>

48 <p>We can find the LCM of 30 by listing the multiples of 3, 5 and 10, and finding the least common multiple.</p>

50 <p>Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33….</p>

49 <p>Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33….</p>

51 <p>Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50….</p>

50 <p>Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50….</p>

52 <p>Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90…</p>

51 <p>Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90…</p>

53 <p>The LCM is 30</p>

52 <p>The LCM is 30</p>

54 <p> To find the GCF, list the factors of 3, 5 and 10, and find the GCF. Factors of 3 are 1 and 3, factors of 5 are 1 and 5,</p>

53 <p> To find the GCF, list the factors of 3, 5 and 10, and find the GCF. Factors of 3 are 1 and 3, factors of 5 are 1 and 5,</p>

55 <p>the factors of 10 are 1, 2 and 5. So the GCF is 1.</p>

54 <p>the factors of 10 are 1, 2 and 5. So the GCF is 1.</p>

56 <p>Well explained 👍</p>

55 <p>Well explained 👍</p>

57 <h3>Problem 2</h3>

56 <h3>Problem 2</h3>

58 <p>Runner A runs every 3 minutes in a trail and runner B every 5 minutes and runner C runs every 10 minutes, and both of them start together. When will they both meet at the starting point again?</p>

57 <p>Runner A runs every 3 minutes in a trail and runner B every 5 minutes and runner C runs every 10 minutes, and both of them start together. When will they both meet at the starting point again?</p>

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

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

60 <p> The LCM of 3, 5 and 10 is 30. </p>

59 <p> The LCM of 3, 5 and 10 is 30. </p>

61 <h3>Explanation</h3>

60 <h3>Explanation</h3>

62 <p>Runner A and B will meet at the starting point in 30 minutes, the LCM of 3, 5 and 10 is 30, which is the smallest common time interval for the given digits. </p>

61 <p>Runner A and B will meet at the starting point in 30 minutes, the LCM of 3, 5 and 10 is 30, which is the smallest common time interval for the given digits. </p>

63 <p>Well explained 👍</p>

62 <p>Well explained 👍</p>

64 <h3>Problem 3</h3>

63 <h3>Problem 3</h3>

65 <p>What will be the product when the LCM of 3,5 and 10 is multiplied twice?</p>

64 <p>What will be the product when the LCM of 3,5 and 10 is multiplied twice?</p>

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

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

67 <p> The product will be 900 </p>

66 <p> The product will be 900 </p>

68 <h3>Explanation</h3>

67 <h3>Explanation</h3>

69 <p>The LCM is 30. When 30 is multiplied twice, we get 900 as the product (30 × 30 = 900)</p>

68 <p>The LCM is 30. When 30 is multiplied twice, we get 900 as the product (30 × 30 = 900)</p>

70 <p>Well explained 👍</p>

69 <p>Well explained 👍</p>

71 <h2>FAQs on LCM of 3, 5 and 10</h2>

70 <h2>FAQs on LCM of 3, 5 and 10</h2>

72 <h3>1.What is the LCM of 3 5 10 15?</h3>

71 <h3>1.What is the LCM of 3 5 10 15?</h3>

73 <p>The LCM of 3, 5, 10 and 15 is 30. We can find the LCM using the listing method. Find the multiples of 3, 5, 10 and 15. From the multiple list, find the common multiple that is lower in value.</p>

72 <p>The LCM of 3, 5, 10 and 15 is 30. We can find the LCM using the listing method. Find the multiples of 3, 5, 10 and 15. From the multiple list, find the common multiple that is lower in value.</p>

74 <h3>2.What is the LCM of 3, 4 and 10?</h3>

73 <h3>2.What is the LCM of 3, 4 and 10?</h3>

75 <p>The LCM of 3, 4 and 10 is 60. We can find the LCM using the listing method. Find the multiples of 3, 4, and 10. From the multiple list, find the common multiple that is lower in value. </p>

74 <p>The LCM of 3, 4 and 10 is 60. We can find the LCM using the listing method. Find the multiples of 3, 4, and 10. From the multiple list, find the common multiple that is lower in value. </p>

76 <h3>3.Is the LCM of 3 and 5 15?</h3>

75 <h3>3.Is the LCM of 3 and 5 15?</h3>

77 <p>Yes, the LCM of 3 and 5 is 15. Using the prime factorization, we can find the LCM. The prime factorization of 3 and 5 is 31 and 51. Multiply them to get 15 as the LCM. </p>

76 <p>Yes, the LCM of 3 and 5 is 15. Using the prime factorization, we can find the LCM. The prime factorization of 3 and 5 is 31 and 51. Multiply them to get 15 as the LCM. </p>

78 <h3>4.What is the LCM of 3, 5 and 9?</h3>

77 <h3>4.What is the LCM of 3, 5 and 9?</h3>

79 <p>The LCM of 3, 5 and 9 is 45. Make use of the listing method to find the LCM. Find the multiples of 3, 5 and 9. From the list, identify the common multiple having lower value. </p>

78 <p>The LCM of 3, 5 and 9 is 45. Make use of the listing method to find the LCM. Find the multiples of 3, 5 and 9. From the list, identify the common multiple having lower value. </p>

80 <h3>5. What is the LCM of 12 and 24?</h3>

79 <h3>5. What is the LCM of 12 and 24?</h3>

81 <p>The LCM of 12 and 24 is 24. Make use of the listing method to find the LCM. Find the multiples of 12 and 24. From the list, identify the common multiple having lower value. </p>

80 <p>The LCM of 12 and 24 is 24. Make use of the listing method to find the LCM. Find the multiples of 12 and 24. From the list, identify the common multiple having lower value. </p>

82 <h2>Important Glossaries for LCM of 3,5 and 10</h2>

81 <h2>Important Glossaries for LCM of 3,5 and 10</h2>

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

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

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

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

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

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

86 </ul><ul><li><strong>LCM:</strong>The least common multiple is the smallest number divisible by two or more numbers. </li>

85 </ul><ul><li><strong>LCM:</strong>The least common multiple is the smallest number divisible by two or more numbers. </li>

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

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

88 <p>▶</p>

87 <p>▶</p>

89 <h2>Hiralee Lalitkumar Makwana</h2>

88 <h2>Hiralee Lalitkumar Makwana</h2>

90 <h3>About the Author</h3>

89 <h3>About the Author</h3>

91 <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>

90 <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>

92 <h3>Fun Fact</h3>

91 <h3>Fun Fact</h3>

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

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