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2 Last updated onAugust 5, 2025

3 The Least common multiple (LCM) is the smallest number that is divisible by the numbers 15,20 and 25. 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.

4 <h2>What is the LCM of 15,20 and 25?</h2>

5 <h2>How to find the LCM of 15,20 and 25?</h2>

6 There are various methods to find the LCM, Listing method,<a>prime factorization</a>method and<a>division</a>method are explained below;

7 <h3>LCM of 15,20 and 25 using the Listing Multiples Method</h3>

8 The LCM of 15,20 and 25 can be found using the following steps:

9 Step1:Write down the multiples of each number

10 Multiples of 15 = 15,30,45,60,75,90,105,120,135,150,165,180…300

11 Multiples of 20= 20,40,60,80,100,120,140,160,180,…300

12 Multiples of 25 = 25,50,75,100,125,150,175,200…300

13 Step2:Ascertain the smallest multiple from the listed multiples

14 The smallest<a>common multiple</a>is 300

15 Thus, LCM (15,20,25) = 300

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18 <h3>LCM of 15,20 and 25 using the Prime Factorization Method</h3>

17 <h3>LCM of 15,20 and 25 using the Prime Factorization Method</h3>

19 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.

18 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.

20 Step 1: Find the prime factors of the numbers:

19 Step 1: Find the prime factors of the numbers:

21 Prime factorization of 15 = 5×3

20 Prime factorization of 15 = 5×3

22 Prime factorization of 20 = 5×2×2

21 Prime factorization of 20 = 5×2×2

23 Prime factorization of 25 = 5×5

22 Prime factorization of 25 = 5×5

24

23

25 Step2: Take the highest powers of each prime factor, and multiply the highest powers to get the LCM:

24 Step2: Take the highest powers of each prime factor, and multiply the highest powers to get the LCM:

26 5×3×2×2×5 = 300

25 5×3×2×2×5 = 300

27 LCM (15,20,25) = 300

26 LCM (15,20,25) = 300

28 <h3>LCM of 15,20 and 25 using the Division Method</h3>

27 <h3>LCM of 15,20 and 25 using the Division Method</h3>

29 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.

28 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.

30 Step 1: Write the numbers, divide by common prime factors and multiply the divisors.

29 Step 1: Write the numbers, divide by common prime factors and multiply the divisors.

31 Step 2: 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.bring down the numbers not divisible by the previously chosen<a>prime number</a>.

30 Step 2: 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.bring down the numbers not divisible by the previously chosen<a>prime number</a>.

32 Step 3:Continue dividing the numbers until the last row of the results is ‘1’ .

31 Step 3:Continue dividing the numbers until the last row of the results is ‘1’ .

33 2×2×3×5×5 = 300

32 2×2×3×5×5 = 300

34 Thus, LCM (15,20,25) =300

33 Thus, LCM (15,20,25) =300

35 <h2>Common Mistakes and how to avoid them while finding the LCM of 15,20 and 25</h2>

34 <h2>Common Mistakes and how to avoid them while finding the LCM of 15,20 and 25</h2>

36 Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 15,20 and 25, make a note

35 Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 15,20 and 25, make a note

37 while practising.

36 while practising.

38 <h3>Problem 1</h3>

37 <h3>Problem 1</h3>

39 LCM of 15 and x is 60. Find x.

38 LCM of 15 and x is 60. Find x.

40 Okay, lets begin

39 Okay, lets begin

41 LCM(15,x) = 60

40 LCM(15,x) = 60

42 LCM(a,b)=a×b/HCF(a,b)

41 LCM(a,b)=a×b/HCF(a,b)

43 Let x be;

42 Let x be;

44 LCM(15,x) = 15×x/HCF(15,x) = 60

43 LCM(15,x) = 15×x/HCF(15,x) = 60

45 Let’s analyze x as;

44 Let’s analyze x as;

46 Prime factorization of 15 = 5×3

45 Prime factorization of 15 = 5×3

47 Prime factorization of 60 = 5×2×2×3

46 Prime factorization of 60 = 5×2×2×3

48 For the LCM to be 60, x should contribute 22 to the LCM;

47 For the LCM to be 60, x should contribute 22 to the LCM;

49 x could be 20; 22×5 = 20

48 x could be 20; 22×5 = 20

50 Let us now verify the above assumption;

49 Let us now verify the above assumption;

51 HCF(15,20) = 5

50 HCF(15,20) = 5

52 LCM(15,20) = 15×20/5= 60

51 LCM(15,20) = 15×20/5= 60

53 <h3>Explanation</h3>

52 <h3>Explanation</h3>

54 After the above verification, we can say that the missing number is 20.

53 After the above verification, we can say that the missing number is 20.

55 Well explained 👍

54 Well explained 👍

56 <h3>Problem 2</h3>

55 <h3>Problem 2</h3>

57 LCM (15,20,25) = x. Find the smallest positive integer (n), where n×x is a multiple of 60.

56 LCM (15,20,25) = x. Find the smallest positive integer (n), where n×x is a multiple of 60.

58 Okay, lets begin

57 Okay, lets begin

59 LCM (15,20,25) = x

58 LCM (15,20,25) = x

60 We ascertained the LCM of 15,20,25 from the previous calculations.

59 We ascertained the LCM of 15,20,25 from the previous calculations.

61 LCM (15,20,25) = 300

60 LCM (15,20,25) = 300

62 n is;

61 n is;

63 n×300 is a multiple of 60

62 n×300 is a multiple of 60

64 Te same can be rearranged as;

63 Te same can be rearranged as;

65 n×300 = k×60, for some integer k

64 n×300 = k×60, for some integer k

66 Divide both the sides 60;

65 Divide both the sides 60;

67 n×5 = k

66 n×5 = k

68 n×5 = k implies that n is to be a multiple of 12, 300/60 = 5 and n to be a multiple of 1/5.

67 n×5 = k implies that n is to be a multiple of 12, 300/60 = 5 and n to be a multiple of 1/5.

69 Smallest n =12

68 Smallest n =12

70 <h3>Explanation</h3>

69 <h3>Explanation</h3>

71 n is 12, as elaborated above. It satisfies the condition laid the smallest positive integer (n), where n×x is a multiple of 60.

70 n is 12, as elaborated above. It satisfies the condition laid the smallest positive integer (n), where n×x is a multiple of 60.

72 Well explained 👍

71 Well explained 👍

73 <h3>Problem 3</h3>

72 <h3>Problem 3</h3>

74 a =15, b=20, c=25, use the formula for the LCM of three numbers.

73 a =15, b=20, c=25, use the formula for the LCM of three numbers.

75 Okay, lets begin

74 Okay, lets begin

76 The formula used to find the LCM of 3 digits is;

75 The formula used to find the LCM of 3 digits is;

77 LCM(a,b,c) = LCM(a,b)×c/HCF(LCM(a,b)c)

76 LCM(a,b,c) = LCM(a,b)×c/HCF(LCM(a,b)c)

78 To apply the above formula, calculate the LCM of 15 and 20 first;

77 To apply the above formula, calculate the LCM of 15 and 20 first;

79 Prime factorization of 15 = 5×3

78 Prime factorization of 15 = 5×3

80 Prime factorization of 20 = 5×4

79 Prime factorization of 20 = 5×4

81 LCM (15,20) = 60

80 LCM (15,20) = 60

82 Next, find the HCF of 60 (LCM of 15 and 20) and 25;

81 Next, find the HCF of 60 (LCM of 15 and 20) and 25;

83 Factors of 60 = 1,2,3,4,5,6,10,12,15,20,30,60

82 Factors of 60 = 1,2,3,4,5,6,10,12,15,20,30,60

84 Factors of 25 = 1,5,25

83 Factors of 25 = 1,5,25

85 HCF(60,25) = 5

84 HCF(60,25) = 5

86 We can now substitute the ascertained values into the formula;

85 We can now substitute the ascertained values into the formula;

87 LCM(a,b,c) = LCM(a,b)×c/HCF(LCM(a,b)c)

86 LCM(a,b,c) = LCM(a,b)×c/HCF(LCM(a,b)c)

88 LCM(15,20,25) = LCM(15,20)×25/5

87 LCM(15,20,25) = LCM(15,20)×25/5

89 LCM(15,20,25) = 60×25/5 = 300

88 LCM(15,20,25) = 60×25/5 = 300

90 <h3>Explanation</h3>

89 <h3>Explanation</h3>

91 The LCM of numbers 15,20,25 using the formula is 300. The above explained is how we ascertain it.

90 The LCM of numbers 15,20,25 using the formula is 300. The above explained is how we ascertain it.

92 Well explained 👍

91 Well explained 👍

93 <h2>FAQs on LCM of 15,20 and 25</h2>

92 <h2>FAQs on LCM of 15,20 and 25</h2>

94 <h3>1.List the multiples of 15,20 and 25.</h3>

93 <h3>1.List the multiples of 15,20 and 25.</h3>

95 Multiples of 15 = 15,30,45,60,75,90,105,120,135,150,165,180…

94 Multiples of 15 = 15,30,45,60,75,90,105,120,135,150,165,180…

96 Multiples of 20= 20,40,60,80,100,120,140,160,180,…

95 Multiples of 20= 20,40,60,80,100,120,140,160,180,…

97 Multiples of 25 = 25,50,75,100,125,150,175,200…

96 Multiples of 25 = 25,50,75,100,125,150,175,200…

98 <h3>2.What is the LCM of 15,20 and 30?</h3>

97 <h3>2.What is the LCM of 15,20 and 30?</h3>

99 Prime factorization of 15 = 5×3

98 Prime factorization of 15 = 5×3

100 Prime factorization of 20 = 5×4

99 Prime factorization of 20 = 5×4

101 Prime factorization of 30 = 5×2×3

100 Prime factorization of 30 = 5×2×3

102 LCM (15,20, 30) = 5×22×3 = 60

101 LCM (15,20, 30) = 5×22×3 = 60

103 <h3>3.What is the LCM of 12,15,20,22 and 25?</h3>

102 <h3>3.What is the LCM of 12,15,20,22 and 25?</h3>

104 Prime factorization of 12 = 2×2×3

103 Prime factorization of 12 = 2×2×3

105 Prime factorization of 15 = 5×3

104 Prime factorization of 15 = 5×3

106 Prime factorization of 20 = 5×2×2

105 Prime factorization of 20 = 5×2×2

107 Prime factorization of 22 = 2×11

106 Prime factorization of 22 = 2×11

108 Prime factorization of 25 = 5×5

107 Prime factorization of 25 = 5×5

109 LCM (12,15,20,22,25) = 22×3×52×11 = 3300

108 LCM (12,15,20,22,25) = 22×3×52×11 = 3300

110 <h3>4. What is the LCM of 15,25 and 45?</h3>

109 <h3>4. What is the LCM of 15,25 and 45?</h3>

111 Prime factorization of 15 = 5×3

110 Prime factorization of 15 = 5×3

112 Prime factorization of 25 = 5×5

111 Prime factorization of 25 = 5×5

113 Prime factorization of 45 = 5×3×3

112 Prime factorization of 45 = 5×3×3

114 LCM (15,25,45) = 225

113 LCM (15,25,45) = 225

115 <h3>5.What is the LCM of 20,25 and 30?</h3>

114 <h3>5.What is the LCM of 20,25 and 30?</h3>

116 Prime factorization of 20 = 5×2×2

115 Prime factorization of 20 = 5×2×2

117 Prime factorization of 25 = 5×5

116 Prime factorization of 25 = 5×5

118 Prime factorization of 30 = 5×2×3

117 Prime factorization of 30 = 5×2×3

119 LCM (20,25,30) = 300

118 LCM (20,25,30) = 300

120 <h2>Important glossaries for the LCM of 15,20 and 25</h2>

119 <h2>Important glossaries for the LCM of 15,20 and 25</h2>

121 Multiple:A number and any integer multiplied.

120 Multiple:A number and any integer multiplied.

122 Prime Factor:A natural number (other than 1) that has factors that are one and itself.

121 Prime Factor:A natural number (other than 1) that has factors that are one and itself.

123 Prime Factorization:The process of breaking down a number into its prime factors is called Prime Factorization.

122 Prime Factorization:The process of breaking down a number into its prime factors is called Prime Factorization.

124 Co-prime numbers:When the only positive integer that is a divisor of them both is 1, a number is co-prime.

123 Co-prime numbers:When the only positive integer that is a divisor of them both is 1, a number is co-prime.

125 What Are Numbers? 🔢 | Fun Explanation with 🎯 Real-Life Examples for Kids | ✨BrightCHAMPS Math

124 What Are Numbers? 🔢 | Fun Explanation with 🎯 Real-Life Examples for Kids | ✨BrightCHAMPS Math

126 ▶

125 ▶

127 <h2>Hiralee Lalitkumar Makwana</h2>

126 <h2>Hiralee Lalitkumar Makwana</h2>

128 <h3>About the Author</h3>

127 <h3>About the Author</h3>

129 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.

128 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.

130 <h3>Fun Fact</h3>

129 <h3>Fun Fact</h3>

131 : She loves to read number jokes and games.

130 : She loves to read number jokes and games.