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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 3 and 5. The LCM can be found using the listing multiples method, the prime factorization and/or division methods. 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 3 and 5?</h2>

5 <h2>How to find the LCM of 3 and 5?</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 3 and 5 using the Listing Multiples Method</h3>

8 <p> The LCM of 3 and 5 can be found using the following steps:</p>

9 <p><strong>Step 1: </strong>Write down the multiples of each number</p>

10 <p>Multiples of 3 = 3,6,9,12,15 …</p>

11 <p>Multiples of 5 = 5, 10,15,20 …</p>

12 <p><strong>Step 2:</strong>Ascertain the smallest multiple from the listed multiples</p>

13 <p>The smallest<a>common multiple</a>is 15.</p>

14 <p>Thus, LCM(3, 5) = 15.</p>

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17 <h3>LCM of 3 and 5 using the Prime Factorization Method</h3>

16 <h3>LCM of 3 and 5 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>Step 1:</strong>Find the prime factors of the numbers:</p>

18 <p><strong>Step 1:</strong>Find the prime factors of the numbers:</p>

20 <p>Prime factorization of 3 = 3</p>

19 <p>Prime factorization of 3 = 3</p>

21 <p>Prime factorization of 5 = 5</p>

20 <p>Prime factorization of 5 = 5</p>

22 <p> Take the highest powers of each prime factor:</p>

21 <p> Take the highest powers of each prime factor:</p>

23 <p>Highest power of 3 = 3</p>

22 <p>Highest power of 3 = 3</p>

24 <p>Highest power of 5 = 5</p>

23 <p>Highest power of 5 = 5</p>

25 <p>Multiply the highest powers to get the LCM:</p>

24 <p>Multiply the highest powers to get the LCM:</p>

26 <p>LCM(3, 5) = 3 × 5 = 15</p>

25 <p>LCM(3, 5) = 3 × 5 = 15</p>

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

26 <h3>LCM of 3 and 5 using the Division Method</h3>

28 <p>This method involves dividing both numbers by their common prime factors until no further division is possible, then multiplying the divisors to find the LCM.</p>

27 <p>This method involves dividing both numbers by their common prime factors until no further division is possible, then multiplying the divisors to find the LCM.</p>

29 <p><strong>Step1:</strong>Write the numbers:</p>

28 <p><strong>Step1:</strong>Write the numbers:</p>

30 <p><strong>Step 2 :</strong> Divide by common prime factors and multiply the divisors: </p>

29 <p><strong>Step 2 :</strong> Divide by common prime factors and multiply the divisors: </p>

31 <p>3 × 5 = 15</p>

30 <p>3 × 5 = 15</p>

32 <p>Thus, LCM(3, 5) = 15.</p>

31 <p>Thus, LCM(3, 5) = 15.</p>

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

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

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

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

35 <h3>Problem 1</h3>

34 <h3>Problem 1</h3>

36 <p>A number n is divisible by 3 and 5. The value of n is between 20 and 40, find n.</p>

35 <p>A number n is divisible by 3 and 5. The value of n is between 20 and 40, find n.</p>

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

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

38 <p>To solve for n, we first find the LCM of the numbers 3 and 5; </p>

37 <p>To solve for n, we first find the LCM of the numbers 3 and 5; </p>

39 <p>Prime factorization of 3 = 31</p>

38 <p>Prime factorization of 3 = 31</p>

40 <p>Prime factorization of 5 = 51</p>

39 <p>Prime factorization of 5 = 51</p>

41 <p>LCM (3,5) = 15 </p>

40 <p>LCM (3,5) = 15 </p>

42 <p>15×2 = 30, a multiple of both 3 and 5. </p>

41 <p>15×2 = 30, a multiple of both 3 and 5. </p>

43 <h3>Explanation</h3>

42 <h3>Explanation</h3>

44 <p>We find a multiple of 15, that falls in the range of 20 and 40 is; 15 ×2 = 30, which is divisible by both 3 and 5. </p>

43 <p>We find a multiple of 15, that falls in the range of 20 and 40 is; 15 ×2 = 30, which is divisible by both 3 and 5. </p>

45 <p>Well explained 👍</p>

44 <p>Well explained 👍</p>

46 <h3>Problem 2</h3>

45 <h3>Problem 2</h3>

47 <p>Verify a×b = LCM (a,b) ×HCF(a,b) for 3 and 5.</p>

46 <p>Verify a×b = LCM (a,b) ×HCF(a,b) for 3 and 5.</p>

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

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

49 <p>a = 3, b= 5 </p>

48 <p>a = 3, b= 5 </p>

50 <p>a×b = LCM (a,b) ×HCF(a,b)</p>

49 <p>a×b = LCM (a,b) ×HCF(a,b)</p>

51 <p>3×5 = LCM (3,5) ×HCF(3,5)</p>

50 <p>3×5 = LCM (3,5) ×HCF(3,5)</p>

52 <p>15 = 15 ×1</p>

51 <p>15 = 15 ×1</p>

53 <p>15 = 15</p>

52 <p>15 = 15</p>

54 <h3>Explanation</h3>

53 <h3>Explanation</h3>

55 <p>LHS = RHS in the above solution, the relationship is hence verified.</p>

54 <p>LHS = RHS in the above solution, the relationship is hence verified.</p>

56 <p>Well explained 👍</p>

55 <p>Well explained 👍</p>

57 <h3>Problem 3</h3>

56 <h3>Problem 3</h3>

58 <p>The product of a and b is 45, and the HCF is 1. a = 3, find the LCM.</p>

57 <p>The product of a and b is 45, and the HCF is 1. a = 3, find the LCM.</p>

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

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

60 <p>We know that; a×b = LCM (a,b) ×HCF(a,b)</p>

59 <p>We know that; a×b = LCM (a,b) ×HCF(a,b)</p>

61 <p>Given; 3×b = 45, HCF(3,b)= 1</p>

60 <p>Given; 3×b = 45, HCF(3,b)= 1</p>

62 <p>Applying the same in the formula; </p>

61 <p>Applying the same in the formula; </p>

63 <p>45 = LCM (3,b) ×1</p>

62 <p>45 = LCM (3,b) ×1</p>

64 <p>LCM (3,b) = 45/1 = 45</p>

63 <p>LCM (3,b) = 45/1 = 45</p>

65 <p>Now we solve for b - 3×b = 45</p>

64 <p>Now we solve for b - 3×b = 45</p>

66 <p>b = 45/3 = 15 </p>

65 <p>b = 45/3 = 15 </p>

67 <h3>Explanation</h3>

66 <h3>Explanation</h3>

68 <p>The other number is 15, LCM(3,15) = 15. </p>

67 <p>The other number is 15, LCM(3,15) = 15. </p>

69 <p>Well explained 👍</p>

68 <p>Well explained 👍</p>

70 <h3>Problem 4</h3>

69 <h3>Problem 4</h3>

71 <p>A car mechanic services a red car every 3 days and a blue car every 5 days. If the cars are serviced today, when will they be serviced next together?</p>

70 <p>A car mechanic services a red car every 3 days and a blue car every 5 days. If the cars are serviced today, when will they be serviced next together?</p>

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

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

73 <p> The LCM of 3 and 5 is 15. </p>

72 <p> The LCM of 3 and 5 is 15. </p>

74 <h3>Explanation</h3>

73 <h3>Explanation</h3>

75 <p> Both cars will be serviced again in 15 days, which is the smallest time interval between the digits. </p>

74 <p> Both cars will be serviced again in 15 days, which is the smallest time interval between the digits. </p>

76 <p>Well explained 👍</p>

75 <p>Well explained 👍</p>

77 <h2>FAQs on the LCM 3 and 5</h2>

76 <h2>FAQs on the LCM 3 and 5</h2>

78 <h3>1.What are the first two LCMs of the numbers 3 and 5 ?</h3>

77 <h3>1.What are the first two LCMs of the numbers 3 and 5 ?</h3>

79 <p>Write down the multiples of each number</p>

78 <p>Write down the multiples of each number</p>

80 <ul><li> Multiples of 3 = 3,6,9,12,15,18,21,24,27,30 …</li>

79 <ul><li> Multiples of 3 = 3,6,9,12,15,18,21,24,27,30 …</li>

81 </ul><ul><li>Multiples of 5 = 5, 10,15,20,25,30 …</li>

80 </ul><ul><li>Multiples of 5 = 5, 10,15,20,25,30 …</li>

82 </ul><ul><li> Ascertain the smallest multiple from the listed multiple</li>

81 </ul><ul><li> Ascertain the smallest multiple from the listed multiple</li>

83 </ul><ul><li>The first smallest common multiple is 15 followed by 30. </li>

82 </ul><ul><li>The first smallest common multiple is 15 followed by 30. </li>

84 </ul><h3>2.What is the Least common denominator (LCD) of 3 and 5 ?</h3>

83 </ul><h3>2.What is the Least common denominator (LCD) of 3 and 5 ?</h3>

85 <p>Both 3 and 5 are prime numbers and share no common factors, therefore, the LCD is 3x5=15. </p>

84 <p>Both 3 and 5 are prime numbers and share no common factors, therefore, the LCD is 3x5=15. </p>

86 <h3>3.What do 3 and 5 have in common ?</h3>

85 <h3>3.What do 3 and 5 have in common ?</h3>

87 <p>The only common factor of 3 and 5 is 1, the given numbers are prime. </p>

86 <p>The only common factor of 3 and 5 is 1, the given numbers are prime. </p>

88 <p>The common multiples of 3 and 5 are; 15,30,45,…</p>

87 <p>The common multiples of 3 and 5 are; 15,30,45,…</p>

89 <h3>4.What is the LCM of 3,5 and 7?</h3>

88 <h3>4.What is the LCM of 3,5 and 7?</h3>

90 <p>There are no common factors between the numbers, as they are all prime. LCM of the numbers = 3×5×7 = 105 </p>

89 <p>There are no common factors between the numbers, as they are all prime. LCM of the numbers = 3×5×7 = 105 </p>

91 <h3>5.How to find multiples of 3 and 5 ?</h3>

90 <h3>5.How to find multiples of 3 and 5 ?</h3>

92 <p>A simple way to find the multiples is adding the number to the next digit. </p>

91 <p>A simple way to find the multiples is adding the number to the next digit. </p>

93 <p>Begin with 3, and keep adding the same multiple fold, do the same for 5. </p>

92 <p>Begin with 3, and keep adding the same multiple fold, do the same for 5. </p>

94 <p>Multiples of 3 = 3,6,9,12,15,18,21,24,27,30 …</p>

93 <p>Multiples of 3 = 3,6,9,12,15,18,21,24,27,30 …</p>

95 <p>Multiples of 5 = 5, 10,15,20,25,30 … </p>

94 <p>Multiples of 5 = 5, 10,15,20,25,30 … </p>

96 <h2>Hiralee Lalitkumar Makwana</h2>

95 <h2>Hiralee Lalitkumar Makwana</h2>

97 <h3>About the Author</h3>

96 <h3>About the Author</h3>

98 <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>

97 <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>

99 <h3>Fun Fact</h3>

98 <h3>Fun Fact</h3>

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

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