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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 18 and 30. In this article, we will learn more about the LCM and how to find the LCM of 18 and 30 using different methods.</p>

4 <h2>What is the LCM of 18 and 30?</h2>

5 <h2>How to find the LCM of 18 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 18 and 30 using the Listing multiples method</h3>

8 <p>The LCM of 18 and 30 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 18 = 18,36,54,72,90,…</p>

11 <p>Multiples of 30 = 30,60,90,…</p>

12 <p><strong>Step 2:</strong>Ascertain the smallest multiple from the listed multiples of 18 and 30. The<a>least common multiple</a>of the numbers 18 and 30 is 90.</p>

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15 <h3>LCM of 18 and 30 using the Prime Factorization</h3>

14 <h3>LCM of 18 and 30 using the Prime Factorization</h3>

16 <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>

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

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

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

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

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

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

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

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

21 <p>LCM (18,30) = 90</p>

20 <p>LCM (18,30) = 90</p>

22 <h3>LCM of 18 and 30 using the Division Method</h3>

21 <h3>LCM of 18 and 30 using the Division Method</h3>

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

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

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

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

25 <p><strong>Step 2:</strong>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.</p>

24 <p><strong>Step 2:</strong>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.</p>

26 <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<a>prime number</a>.</p>

25 <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<a>prime number</a>.</p>

27 <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, LCM (18,30) = 90</p>

26 <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, LCM (18,30) = 90</p>

28 <h2>Common Mistakes and how to avoid them while finding the LCM of 18 and 30</h2>

27 <h2>Common Mistakes and how to avoid them while finding the LCM of 18 and 30</h2>

29 <p>Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 18 and 30, make a note while practicing. </p>

28 <p>Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 18 and 30, make a note while practicing. </p>

30 <h3>Problem 1</h3>

29 <h3>Problem 1</h3>

31 <p>LCM of a and b is 90. a=18, find b.</p>

30 <p>LCM of a and b is 90. a=18, find b.</p>

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

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

33 <p>LCM(18,b) = 90 </p>

32 <p>LCM(18,b) = 90 </p>

34 <p>We apply the below formula to find the missing number; </p>

33 <p>We apply the below formula to find the missing number; </p>

35 <p>LCM(a,b)×HCF(a,b)=a×b</p>

34 <p>LCM(a,b)×HCF(a,b)=a×b</p>

36 <p>With the given figures, we rearrange the formula as;</p>

35 <p>With the given figures, we rearrange the formula as;</p>

37 <p> 90×HCF(18,b) = 18×b </p>

36 <p> 90×HCF(18,b) = 18×b </p>

38 <h3>Explanation</h3>

37 <h3>Explanation</h3>

39 <p>b must have the prime factors 2,3 and 5, for the LCM of 18 and b to be equal to 90. The number with the mentioned as its factors is 30. </p>

38 <p>b must have the prime factors 2,3 and 5, for the LCM of 18 and b to be equal to 90. The number with the mentioned as its factors is 30. </p>

40 <p>Verifying LCM(18,30) = 90 </p>

39 <p>Verifying LCM(18,30) = 90 </p>

41 <p>Therefore, we can conclude that the missing number is 30. </p>

40 <p>Therefore, we can conclude that the missing number is 30. </p>

42 <p>Well explained 👍</p>

41 <p>Well explained 👍</p>

43 <h3>Problem 2</h3>

42 <h3>Problem 2</h3>

44 <p>Verify the relationship between the LCM and HCF of 18 and 30.</p>

43 <p>Verify the relationship between the LCM and HCF of 18 and 30.</p>

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

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

46 <p>We apply the formula → LCM(a,b)×HCF(a,b)=a×b to check the relationship between thew numbers; </p>

45 <p>We apply the formula → LCM(a,b)×HCF(a,b)=a×b to check the relationship between thew numbers; </p>

47 <p>LCM of 18 and 30;</p>

46 <p>LCM of 18 and 30;</p>

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

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

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

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

50 <p>LCM (18,30) = 90</p>

49 <p>LCM (18,30) = 90</p>

51 <p>HCF of 18 and 30; </p>

50 <p>HCF of 18 and 30; </p>

52 <p>Factors of 18 = 1,2,3,6,9,18 </p>

51 <p>Factors of 18 = 1,2,3,6,9,18 </p>

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

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

54 <p>HCF(18,30) = 6</p>

53 <p>HCF(18,30) = 6</p>

55 <p>Now, verifying the same; </p>

54 <p>Now, verifying the same; </p>

56 <p>LCM(a,b)×HCF(a,b)=a×b</p>

55 <p>LCM(a,b)×HCF(a,b)=a×b</p>

57 <p>90×6=18×30</p>

56 <p>90×6=18×30</p>

58 <p>540=540 </p>

57 <p>540=540 </p>

59 <h3>Explanation</h3>

58 <h3>Explanation</h3>

60 <p>The above is how we ascertain and verify the relationship between the LCM and the HCF of two given numbers. It is based on the principle that the product of the HCF and the LCM is equal to the product of the numbers a and b themselves. </p>

59 <p>The above is how we ascertain and verify the relationship between the LCM and the HCF of two given numbers. It is based on the principle that the product of the HCF and the LCM is equal to the product of the numbers a and b themselves. </p>

61 <p>Well explained 👍</p>

60 <p>Well explained 👍</p>

62 <h3>Problem 3</h3>

61 <h3>Problem 3</h3>

63 <p>The LCM of a and b is 90. a=18, what could be the smallest value of b? The HCF of the numbers a and b is a divisor of 6.</p>

62 <p>The LCM of a and b is 90. a=18, what could be the smallest value of b? The HCF of the numbers a and b is a divisor of 6.</p>

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

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

65 <p>LCM(18,b) = 90 </p>

64 <p>LCM(18,b) = 90 </p>

66 <p>HCF (18,b) → a divisor of 6</p>

65 <p>HCF (18,b) → a divisor of 6</p>

67 <p>Possible values of the HCF could be → 1,2,3,6 (factors of 6) </p>

66 <p>Possible values of the HCF could be → 1,2,3,6 (factors of 6) </p>

68 <p>Now we try the factors to fit the condition;</p>

67 <p>Now we try the factors to fit the condition;</p>

69 <p> When HCF = 1, </p>

68 <p> When HCF = 1, </p>

70 <p>LCM(a,b)×HCF(a,b)=a×b</p>

69 <p>LCM(a,b)×HCF(a,b)=a×b</p>

71 <p>LCM(18,b)×HCF(18,b)=18×b</p>

70 <p>LCM(18,b)×HCF(18,b)=18×b</p>

72 <p>90×1 =18×b → b = 90/18 = 5 </p>

71 <p>90×1 =18×b → b = 90/18 = 5 </p>

73 <p>LCM (18,5) = 90, but 5 is not a divisor of 6, this case is invalid. </p>

72 <p>LCM (18,5) = 90, but 5 is not a divisor of 6, this case is invalid. </p>

74 <p>When HCF= 6, </p>

73 <p>When HCF= 6, </p>

75 <p>LCM(a,b)×HCF(a,b)=a×b</p>

74 <p>LCM(a,b)×HCF(a,b)=a×b</p>

76 <p>LCM(18,b)×HCF(18,b)=18×b</p>

75 <p>LCM(18,b)×HCF(18,b)=18×b</p>

77 <p>90×6 =18×b → b = 30 </p>

76 <p>90×6 =18×b → b = 30 </p>

78 <h3>Explanation</h3>

77 <h3>Explanation</h3>

79 <p> b=30, satisfies both the conditions, i.e., the LCM = 90, 30 is a divisor of 6. </p>

78 <p> b=30, satisfies both the conditions, i.e., the LCM = 90, 30 is a divisor of 6. </p>

80 <p>Well explained 👍</p>

79 <p>Well explained 👍</p>

81 <h3>Problem 4</h3>

80 <h3>Problem 4</h3>

82 <p>FAQs on the LCM of 18 and 30</p>

81 <p>FAQs on the LCM of 18 and 30</p>

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

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

84 <p>What is the HCF of 28 and 30 ? </p>

83 <p>What is the HCF of 28 and 30 ? </p>

85 <h3>Explanation</h3>

84 <h3>Explanation</h3>

86 <p>Factors of 28 = 1,2,4,7,14,28 </p>

85 <p>Factors of 28 = 1,2,4,7,14,28 </p>

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

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

88 <p>HCF (28,30) = 2 </p>

87 <p>HCF (28,30) = 2 </p>

89 <p>Well explained 👍</p>

88 <p>Well explained 👍</p>

90 <h3>Problem 5</h3>

89 <h3>Problem 5</h3>

91 <p>What is the ratio between the HCF and LCM of 18 and 30?</p>

90 <p>What is the ratio between the HCF and LCM of 18 and 30?</p>

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

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

93 <p>HCF(18,30) = 6 </p>

92 <p>HCF(18,30) = 6 </p>

94 <p>LCM (8,30) = 90 </p>

93 <p>LCM (8,30) = 90 </p>

95 <p>Ratio = 90/6=15 </p>

94 <p>Ratio = 90/6=15 </p>

96 <h3>Explanation</h3>

95 <h3>Explanation</h3>

97 <p>What is the LCM of 18,24 and 30?</p>

96 <p>What is the LCM of 18,24 and 30?</p>

98 <p>Well explained 👍</p>

97 <p>Well explained 👍</p>

99 <h2>Important glossaries for LCM of 18 and 30</h2>

98 <h2>Important glossaries for LCM of 18 and 30</h2>

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

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

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

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

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

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

103 </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>

102 </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>

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

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

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

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

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

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

107 <p>▶</p>

106 <p>▶</p>

108 <h2>Hiralee Lalitkumar Makwana</h2>

107 <h2>Hiralee Lalitkumar Makwana</h2>

109 <h3>About the Author</h3>

108 <h3>About the Author</h3>

110 <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 <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>

111 <h3>Fun Fact</h3>

110 <h3>Fun Fact</h3>

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

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