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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 5 and 9. 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 5 and 9?</h2>

5 <h2>How to Find the LCM of 5 and 9?</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 <p>LCM of 5 and 9 using the Listing Multiples Method</p>

8 <p>The LCM of 5 and 9 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 5 = 5,10,15,20,25,30,35,40,45,…</p>

11 <p>Multiples of 9 = 9, 18, 27, 36,45,54, …</p>

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

13 <p>The<a>least common multiple</a>is 45.</p>

14 <h3>LCM of 5 and 9 using the Prime Factorization Method</h3>

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>

16 <p><strong>Step1:</strong> Find the prime factors of the numbers</p>

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

18 <p>Prime factorization of 9 = 3 × 3</p>

19 <p><strong>Step2:</strong> Take the highest powers of each prime factor</p>

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

21 <p>Highest power of 9 = 32</p>

22 <p><strong>Step3 :</strong> Multiply the highest powers to get the LCM: </p>

23 <p> LCM(5, 9) = 5×32 = 45</p>

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26 <h2>LCM of 5 and 9 using the Division Method</h2>

25 <h2>LCM of 5 and 9 using the Division Method</h2>

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>

26 <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>

28 <p><strong>Step 1:</strong> Write the numbers, divide by common prime factors and multiply the divisors.</p>

27 <p><strong>Step 1:</strong> Write the numbers, divide by common prime factors and multiply the divisors.</p>

29 <p><strong>Step 2 :</strong>keep dividing till we get 1 as<a>remainder</a>.</p>

28 <p><strong>Step 2 :</strong>keep dividing till we get 1 as<a>remainder</a>.</p>

30 <p>5 × 3 × 3 = 45</p>

29 <p>5 × 3 × 3 = 45</p>

31 <p>Thus, LCM(5, 9) = 45 </p>

30 <p>Thus, LCM(5, 9) = 45 </p>

32 <h2>Common Mistakes and how to avoid them in LCM of 5 and 9</h2>

31 <h2>Common Mistakes and how to avoid them in LCM of 5 and 9</h2>

33 <p>Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 5 and 9, make a note while practicing. </p>

32 <p>Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 5 and 9, make a note while practicing. </p>

34 <h3>Problem 1</h3>

33 <h3>Problem 1</h3>

35 <p>LCM of a and b is 45. a=5, find b.</p>

34 <p>LCM of a and b is 45. a=5, find b.</p>

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

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

37 <p>We can find the value of b using → LCM(a,b) = a×b/HCF(a,b)</p>

36 <p>We can find the value of b using → LCM(a,b) = a×b/HCF(a,b)</p>

38 <p>LCM(a,b)= 45 </p>

37 <p>LCM(a,b)= 45 </p>

39 <p>45=5×b/1 </p>

38 <p>45=5×b/1 </p>

40 <p>Now we solve for b. </p>

39 <p>Now we solve for b. </p>

41 <p>b = 45/5 = 9</p>

40 <p>b = 45/5 = 9</p>

42 <h3>Explanation</h3>

41 <h3>Explanation</h3>

43 <p> By following the above we ascertain the missing digit from the given LCM.</p>

42 <p> By following the above we ascertain the missing digit from the given LCM.</p>

44 <p>Well explained 👍</p>

43 <p>Well explained 👍</p>

45 <h3>Problem 2</h3>

44 <h3>Problem 2</h3>

46 <p>LCM(a,b)×HCF(a,b) = a×b, verify the relationship between the HCF and LCM of 5 and 9 using the given formula.</p>

45 <p>LCM(a,b)×HCF(a,b) = a×b, verify the relationship between the HCF and LCM of 5 and 9 using the given formula.</p>

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

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

48 <p>LCM(a,b)×HCF(a,b) = a×b</p>

47 <p>LCM(a,b)×HCF(a,b) = a×b</p>

49 <p>LCM of 5,9; </p>

48 <p>LCM of 5,9; </p>

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

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

51 <p>Prime factorization of 9 = 3 × 3</p>

50 <p>Prime factorization of 9 = 3 × 3</p>

52 <p>LCM (5,9) = 45 </p>

51 <p>LCM (5,9) = 45 </p>

53 <p>HCF of 5,9; </p>

52 <p>HCF of 5,9; </p>

54 <p>Factors of 5 = 1,5 </p>

53 <p>Factors of 5 = 1,5 </p>

55 <p>Factors of 9 = 1,3,9 </p>

54 <p>Factors of 9 = 1,3,9 </p>

56 <p>HCF(5,9) = 1 </p>

55 <p>HCF(5,9) = 1 </p>

57 <p>Applying the above in the given formula; </p>

56 <p>Applying the above in the given formula; </p>

58 <p>LCM(a,b)×HCF(a,b) = a×b</p>

57 <p>LCM(a,b)×HCF(a,b) = a×b</p>

59 <p>45×1 = 9×5</p>

58 <p>45×1 = 9×5</p>

60 <p>45=45 </p>

59 <p>45=45 </p>

61 <h3>Explanation</h3>

60 <h3>Explanation</h3>

62 <p>LHS=RHS, the relationship stands true in the case of numbers 5 and 9. </p>

61 <p>LHS=RHS, the relationship stands true in the case of numbers 5 and 9. </p>

63 <p>Well explained 👍</p>

62 <p>Well explained 👍</p>

64 <h3>Problem 3</h3>

63 <h3>Problem 3</h3>

65 <p>A yellow bulb is replaced every 5 months and a white bulb is replaced every 9 months. If both of them are replaced today, after how many months will they need to be replaced?</p>

64 <p>A yellow bulb is replaced every 5 months and a white bulb is replaced every 9 months. If both of them are replaced today, after how many months will they need to be replaced?</p>

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

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

67 <p>The LCM of 5 and 9 is 45. </p>

66 <p>The LCM of 5 and 9 is 45. </p>

68 <h3>Explanation</h3>

67 <h3>Explanation</h3>

69 <p>Both bulbs will need replacement together in 9 months. The LCM of 5 and 9 is 45 which is the smallest time interval between the digits. </p>

68 <p>Both bulbs will need replacement together in 9 months. The LCM of 5 and 9 is 45 which is the smallest time interval between the digits. </p>

70 <p>Well explained 👍</p>

69 <p>Well explained 👍</p>

71 <h2>FAQs on LCM of 5 and 9</h2>

70 <h2>FAQs on LCM of 5 and 9</h2>

72 <h3>1.What is the LCD (Lowest common denominator) of 5 and 9?</h3>

71 <h3>1.What is the LCD (Lowest common denominator) of 5 and 9?</h3>

73 <p>LCD of 5 and 9 = 45, the smallest number both 5 and 9 divide into.</p>

72 <p>LCD of 5 and 9 = 45, the smallest number both 5 and 9 divide into.</p>

74 <h3>2.What is the LCM of 7,5 and 9?</h3>

73 <h3>2.What is the LCM of 7,5 and 9?</h3>

75 <p>Find the prime factors of the numbers:</p>

74 <p>Find the prime factors of the numbers:</p>

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

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

77 <p>Prime factorization of 7=7</p>

76 <p>Prime factorization of 7=7</p>

78 <p>Prime factorization of 9 = 3 × 3</p>

77 <p>Prime factorization of 9 = 3 × 3</p>

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

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

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

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

81 <p>Highest power of 7 = 7 </p>

80 <p>Highest power of 7 = 7 </p>

82 <p>Highest power of 9 = 32</p>

81 <p>Highest power of 9 = 32</p>

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

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

84 <p>LCM(5,7, 9) = 5×7×32 = 315 </p>

83 <p>LCM(5,7, 9) = 5×7×32 = 315 </p>

85 <h3>3.What is the LCM of 9,5 and 18?</h3>

84 <h3>3.What is the LCM of 9,5 and 18?</h3>

86 <p> Find the prime factors of the numbers:</p>

85 <p> Find the prime factors of the numbers:</p>

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

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

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

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

89 <p>Prime factorization of 9 = 3 × 3</p>

88 <p>Prime factorization of 9 = 3 × 3</p>

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

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

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

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

92 <p>Highest power of 18 = 32, 2 </p>

91 <p>Highest power of 18 = 32, 2 </p>

93 <p>Highest power of 9 = 32</p>

92 <p>Highest power of 9 = 32</p>

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

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

95 <p> LCM(5,18, 9) = 5×2×32 = 90 </p>

94 <p> LCM(5,18, 9) = 5×2×32 = 90 </p>

96 <h3>4.What is the LCM of 5,9 and 12 ?</h3>

95 <h3>4.What is the LCM of 5,9 and 12 ?</h3>

97 <p>Find the prime factors of the numbers:</p>

96 <p>Find the prime factors of the numbers:</p>

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

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

99 <p>Prime factorization of 12= 3 × 2 × 2</p>

98 <p>Prime factorization of 12= 3 × 2 × 2</p>

100 <p>Prime factorization of 9 = 3 × 3</p>

99 <p>Prime factorization of 9 = 3 × 3</p>

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

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

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

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

103 <p>Highest power of 12 = 22, 3</p>

102 <p>Highest power of 12 = 22, 3</p>

104 <p>Highest power of 9 = 32</p>

103 <p>Highest power of 9 = 32</p>

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

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

106 <p>LCM(5,12, 9) = 5×22×32 = 180 </p>

105 <p>LCM(5,12, 9) = 5×22×32 = 180 </p>

107 <h3>5.What is the HCF of 5 and 9?</h3>

106 <h3>5.What is the HCF of 5 and 9?</h3>

108 <p>5 and 9 share no<a>common factors</a>, therefore the HCF of the numbers 5 and 9 is 1. </p>

107 <p>5 and 9 share no<a>common factors</a>, therefore the HCF of the numbers 5 and 9 is 1. </p>

109 <h2>Important glossaries for LCM of 5 and 9</h2>

108 <h2>Important glossaries for LCM of 5 and 9</h2>

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

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

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

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

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

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

113 </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>

112 </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>

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

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

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

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

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

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

117 <p>▶</p>

116 <p>▶</p>

118 <h2>Hiralee Lalitkumar Makwana</h2>

117 <h2>Hiralee Lalitkumar Makwana</h2>

119 <h3>About the Author</h3>

118 <h3>About the Author</h3>

120 <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>

119 <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>

121 <h3>Fun Fact</h3>

120 <h3>Fun Fact</h3>

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

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