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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 2 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 2 and 9?</h2>

5 <h2>How to Find the LCM of 2 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 <h3>LCM of 2 and 9 using the Listing Multiples Method</h3>

8 <p> The LCM of 2 and 9 can be calculated using the following steps:</p>

9 <p><strong>Steps:</strong></p>

10 <ol><li>Write down the multiples of each number</li>

11 </ol><p> - Multiples of 2 = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, …</p>

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

13 <ol><li>Ascertain the smallest multiple from the listed multiples:</li>

14 </ol><p> - The smallest<a>common multiple</a>is 18.</p>

15 <p>Thus, LCM(2, 9) = 18.</p>

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18 <h3>LCM of 2 and 9 using the Prime Factorization Method</h3>

17 <h3>LCM of 2 and 9 using the Prime Factorization Method</h3>

19 <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>

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>

20 <p><strong>Steps:</strong></p>

19 <p><strong>Steps:</strong></p>

21 <ol><li> Find the prime factors of each number:</li>

20 <ol><li> Find the prime factors of each number:</li>

22 </ol><p> - Prime factorization of 2 = 2</p>

21 </ol><p> - Prime factorization of 2 = 2</p>

23 <p> - Prime factorization of 9 = 3 × 3</p>

22 <p> - Prime factorization of 9 = 3 × 3</p>

24 <ol><li> Take the highest powers of each prime factor:</li>

23 <ol><li> Take the highest powers of each prime factor:</li>

25 </ol><p> - Highest power of 2 = 2¹</p>

24 </ol><p> - Highest power of 2 = 2¹</p>

26 <p> - Highest power of 3 = 3²</p>

25 <p> - Highest power of 3 = 3²</p>

27 <ol><li>Multiply the highest powers to get the LCM:</li>

26 <ol><li>Multiply the highest powers to get the LCM:</li>

28 </ol><p>LCM(2, 9) = 2¹ × 3² = 18.</p>

27 </ol><p>LCM(2, 9) = 2¹ × 3² = 18.</p>

29 <h3>LCM of 2 and 9 using the Division Method</h3>

28 <h3>LCM of 2 and 9 using the Division Method</h3>

30 <p>This method involves dividing both numbers by their common prime factors and multiplying the divisors to find the LCM.</p>

29 <p>This method involves dividing both numbers by their common prime factors and multiplying the divisors to find the LCM.</p>

31 <p><strong>Steps:</strong></p>

30 <p><strong>Steps:</strong></p>

32 <ol><li> Write the numbers, divide by common prime factors and multiply the divisors.</li>

31 <ol><li> Write the numbers, divide by common prime factors and multiply the divisors.</li>

33 </ol><p>Thus, LCM(2, 9) = 18</p>

32 </ol><p>Thus, LCM(2, 9) = 18</p>

34 <h2>Common Mistakes and how to avoid them while finding the LCM of 2 and 9</h2>

33 <h2>Common Mistakes and how to avoid them while finding the LCM of 2 and 9</h2>

35 <p>Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 2 and 9 make a note while practicing.</p>

34 <p>Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 2 and 9 make a note while practicing.</p>

36 <h3>Problem 1</h3>

35 <h3>Problem 1</h3>

37 <p>P visits a café every 2 and Q visits the same every 9 days. On which day are they likely to run into each other?</p>

36 <p>P visits a café every 2 and Q visits the same every 9 days. On which day are they likely to run into each other?</p>

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

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

39 <p>The LCM of 2 and 9 is 18.</p>

38 <p>The LCM of 2 and 9 is 18.</p>

40 <h3>Explanation</h3>

39 <h3>Explanation</h3>

41 <p>They will run into each other on the 18th day. The LCM of 2 and 9 is 18, which is the smallest common time interval for the given digits.</p>

40 <p>They will run into each other on the 18th day. The LCM of 2 and 9 is 18, which is the smallest common time interval for the given digits.</p>

42 <p>Well explained 👍</p>

41 <p>Well explained 👍</p>

43 <h3>Problem 2</h3>

42 <h3>Problem 2</h3>

44 <p>An HP Printer prints a batch every 2 minutes and a Canon printer prints a batch every 9 minutes. If the machines start at 10:00 AM, when will they print out a batch at the same time?</p>

43 <p>An HP Printer prints a batch every 2 minutes and a Canon printer prints a batch every 9 minutes. If the machines start at 10:00 AM, when will they print out a batch at the same time?</p>

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

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

46 <p>The LCM of 2 and 9 is 18.</p>

45 <p>The LCM of 2 and 9 is 18.</p>

47 <h3>Explanation</h3>

46 <h3>Explanation</h3>

48 <p>Both machines will print a batch together at 10:18 AM. The LCM of 2 and 9 is 18, which is the smallest common time interval for the given digits.</p>

47 <p>Both machines will print a batch together at 10:18 AM. The LCM of 2 and 9 is 18, which is the smallest common time interval for the given digits.</p>

49 <p>Well explained 👍</p>

48 <p>Well explained 👍</p>

50 <h3>Problem 3</h3>

49 <h3>Problem 3</h3>

51 <p>In a neighborhood park, the fountain show is turned on every 2 minutes, and the light show every 9 minutes. If both the shows are turned on at the same time, when will they next be turned on together again?</p>

50 <p>In a neighborhood park, the fountain show is turned on every 2 minutes, and the light show every 9 minutes. If both the shows are turned on at the same time, when will they next be turned on together again?</p>

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

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

53 <p> The LCM of 2 and 9 is 18.</p>

52 <p> The LCM of 2 and 9 is 18.</p>

54 <h3>Explanation</h3>

53 <h3>Explanation</h3>

55 <p>Both the shows will turn on at the same time in 18 minutes. The LCM of 2 and 9 is 18, which is the smallest common time interval for the given digits.</p>

54 <p>Both the shows will turn on at the same time in 18 minutes. The LCM of 2 and 9 is 18, which is the smallest common time interval for the given digits.</p>

56 <p>Well explained 👍</p>

55 <p>Well explained 👍</p>

57 <h3>Problem 4</h3>

56 <h3>Problem 4</h3>

58 <p>A car mechanic services a red car every 2 days and a blue car every 9 days. If the cars are serviced today, when will they be serviced next together?</p>

57 <p>A car mechanic services a red car every 2 days and a blue car every 9 days. If the cars are serviced today, when will they be serviced next together?</p>

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

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

60 <p>The LCM of 2 and 9 is 18.</p>

59 <p>The LCM of 2 and 9 is 18.</p>

61 <h3>Explanation</h3>

60 <h3>Explanation</h3>

62 <p>Both cars will be serviced again in 18 days. The LCM of 2 and 9 is 18, which is the smallest common time interval for the given digits.</p>

61 <p>Both cars will be serviced again in 18 days. The LCM of 2 and 9 is 18, which is the smallest common time interval for the given digits.</p>

63 <p>Well explained 👍</p>

62 <p>Well explained 👍</p>

64 <h2>FAQs on LCM of 2 and 9</h2>

63 <h2>FAQs on LCM of 2 and 9</h2>

65 <h3>1.Why is the LCM of 2 and 9 not simply their product (2 × 9 = 18)?</h3>

64 <h3>1.Why is the LCM of 2 and 9 not simply their product (2 × 9 = 18)?</h3>

66 <p> Multiplying gives you the product of the numbers, in this case,18. LCM, however, is the smallest common multiple that can be ascertained following the listing multiples method, prime factorization, or the division method.</p>

65 <p> Multiplying gives you the product of the numbers, in this case,18. LCM, however, is the smallest common multiple that can be ascertained following the listing multiples method, prime factorization, or the division method.</p>

67 <h3>2.How do you find the LCM with different bases in an exponential equation ?</h3>

66 <h3>2.How do you find the LCM with different bases in an exponential equation ?</h3>

68 <p>You can find the LCM For<a>exponential equations</a>with different bases by following the below example,</p>

67 <p>You can find the LCM For<a>exponential equations</a>with different bases by following the below example,</p>

69 <ul><li>Find the LCM of 24<strong>×</strong>92 and 23<strong>×</strong>93</li>

68 <ul><li>Find the LCM of 24<strong>×</strong>92 and 23<strong>×</strong>93</li>

70 <li>Factorize the<a>terms</a>and find the highest power </li>

69 <li>Factorize the<a>terms</a>and find the highest power </li>

71 </ul><p>Highest power of 2 = 24</p>

70 </ul><p>Highest power of 2 = 24</p>

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

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

73 <p>LCM = 24<strong>×</strong>93</p>

72 <p>LCM = 24<strong>×</strong>93</p>

74 <h3>3.What is the LCM formula using the HCF?</h3>

73 <h3>3.What is the LCM formula using the HCF?</h3>

75 <ul><li>The LCM can be found using the<a>formula</a>, and as explained with the example given below. </li>

74 <ul><li>The LCM can be found using the<a>formula</a>, and as explained with the example given below. </li>

76 </ul><p>LCM (a, b)= a×b/HCF(a, b)</p>

75 </ul><p>LCM (a, b)= a×b/HCF(a, b)</p>

77 <p>For 2 and 9, HCF(2,9)= 1</p>

76 <p>For 2 and 9, HCF(2,9)= 1</p>

78 <p>So, LCM(2,9)=2×9/1 = 18</p>

77 <p>So, LCM(2,9)=2×9/1 = 18</p>

79 <h3>4.What is the HCF of 2 and 9?</h3>

78 <h3>4.What is the HCF of 2 and 9?</h3>

80 <ul><li>HCF of 2 and 9 can be found by following the below steps; </li>

79 <ul><li>HCF of 2 and 9 can be found by following the below steps; </li>

81 </ul><ol><li>List down the prime factors of the numbers</li>

80 </ul><ol><li>List down the prime factors of the numbers</li>

82 </ol><ul><li>Prime factors of 2 = 2</li>

81 </ol><ul><li>Prime factors of 2 = 2</li>

83 <li>Prime factors of 9 = 3×3/32</li>

82 <li>Prime factors of 9 = 3×3/32</li>

84 </ul><ol><li>Find the common prime factors -> None </li>

83 </ul><ol><li>Find the common prime factors -> None </li>

85 <li>HCF of 2,9 = 1, as there are no<a>common factors</a>, the HCF of the given numbers is 1. </li>

84 <li>HCF of 2,9 = 1, as there are no<a>common factors</a>, the HCF of the given numbers is 1. </li>

86 </ol><h3>5.What do the numbers 2 and 9 have in common?</h3>

85 </ol><h3>5.What do the numbers 2 and 9 have in common?</h3>

87 <ul><li>2 and 9 do not have any common factors, except 1, which is also the HCF of the numbers. </li>

86 <ul><li>2 and 9 do not have any common factors, except 1, which is also the HCF of the numbers. </li>

88 <li>2 is a<a>prime number</a>, and prime numbers are characterized by have no common factors but 1. </li>

87 <li>2 is a<a>prime number</a>, and prime numbers are characterized by have no common factors but 1. </li>

89 <li>Factors of 9 are 3×3/32, sharing no factors with 2. </li>

88 <li>Factors of 9 are 3×3/32, sharing no factors with 2. </li>

90 </ul><h2>Important glossaries for the LCM of 2 and 9</h2>

89 </ul><h2>Important glossaries for the LCM of 2 and 9</h2>

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

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

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

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

93 <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>

92 <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>

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

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

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

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

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

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

97 <p>▶</p>

96 <p>▶</p>

98 <h2>Hiralee Lalitkumar Makwana</h2>

97 <h2>Hiralee Lalitkumar Makwana</h2>

99 <h3>About the Author</h3>

98 <h3>About the Author</h3>

100 <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 <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>

101 <h3>Fun Fact</h3>

100 <h3>Fun Fact</h3>

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

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