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2 <p>Last updated on<strong>August 5, 2025</strong></p>

3 <p>The LCM comes in use when we need to find a shared pattern between numbers that seem unrelated. We apply LCM to synchronize cycles or schedules, syncing digital signals and finding compatible frequencies in technology. In this article, we’ll take a look at the LCM of 2,3 and 7.</p>

4 <h2>What is the LCM of 2,3 and 7?</h2>

5 <h3>LCM of 2,3 and 7 using the Listing Multiples Method</h3>

6 <p> The LCM of 2,3 and 7 can be found using the following steps:</p>

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

8 <p>Multiples of 2 = 2,4,6,8,10,12,14,…42,…</p>

9 <p>Multiples of 3 = 3,6,9,12,18,…42</p>

10 <p>Multiples of 7 = 7,14,21,28,35,42,…</p>

11 <p>LCM(2,3,7) = 42</p>

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

13 <p>The smallest<a>common multiple</a>is 42.</p>

14 <p>Thus, LCM (2,3,7) = 42</p>

15 <h3>LCM of 2,3 and 7 using the Prime Factorization Method</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>

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

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

19 <p> Prime factorization of 2 = 21</p>

20 <p>Prime factorization of 7 = 71</p>

21 <p><strong>Step 2:</strong>Take the highest powers of each prime factor. Multiply the highest powers to get the LCM</p>

22 <p>LCM(2,3,7) = 42</p>

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25 <h3>LCM of 2,3 and 7 using the Division Method</h3>

24 <h3>LCM of 2,3 and 7 using the Division Method</h3>

26 <ul><li>Write the numbers 2,3 and 7 in a row </li>

25 <ul><li>Write the numbers 2,3 and 7 in a row </li>

27 </ul><ul><li>Divide them by their common prime factors, if there is one</li>

26 </ul><ul><li>Divide them by their common prime factors, if there is one</li>

28 </ul><ul><li>Carry forward the numbers that are left undivided by the previously chosen factor</li>

27 </ul><ul><li>Carry forward the numbers that are left undivided by the previously chosen factor</li>

29 </ul><ul><li>Continue dividing until the<a>remainder</a>is ‘1’ </li>

28 </ul><ul><li>Continue dividing until the<a>remainder</a>is ‘1’ </li>

30 </ul><ul><li>Multiply the divisors to find the LCM</li>

29 </ul><ul><li>Multiply the divisors to find the LCM</li>

31 </ul><ul><li>LCM (2,3,7) = 42</li>

30 </ul><ul><li>LCM (2,3,7) = 42</li>

32 </ul><h2>Common Mistakes and how to avoid them while finding the LCM of 2,3 and 7</h2>

31 </ul><h2>Common Mistakes and how to avoid them while finding the LCM of 2,3 and 7</h2>

33 <p>It is not unusual that kids make mistakes when trying to find the LCM of the numbers 4,5 and 7. This may be due to unclear understanding of the concept or confusion. Make sure to avoid these! </p>

32 <p>It is not unusual that kids make mistakes when trying to find the LCM of the numbers 4,5 and 7. This may be due to unclear understanding of the concept or confusion. Make sure to avoid these! </p>

34 <h3>Problem 1</h3>

33 <h3>Problem 1</h3>

35 <p>LCM (2,6,7) = LCM(2,3,7) → Verify.</p>

34 <p>LCM (2,6,7) = LCM(2,3,7) → Verify.</p>

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

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

37 <p>LCM of 2,6,7; </p>

36 <p>LCM of 2,6,7; </p>

38 <p>Prime factorization of 2 = 21 </p>

37 <p>Prime factorization of 2 = 21 </p>

39 <p>Prime factorization of 6 = 21×31</p>

38 <p>Prime factorization of 6 = 21×31</p>

40 <p>Prime factorization of 7 = 71</p>

39 <p>Prime factorization of 7 = 71</p>

41 <p>LCM(2,6,7) = 42 </p>

40 <p>LCM(2,6,7) = 42 </p>

42 <p>LCM of 2,3,7; </p>

41 <p>LCM of 2,3,7; </p>

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

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

44 <p>Prime factorization of 2 = 21</p>

43 <p>Prime factorization of 2 = 21</p>

45 <p>Prime factorization of 7 = 71</p>

44 <p>Prime factorization of 7 = 71</p>

46 <p>LCM(2,3,7) = 42 </p>

45 <p>LCM(2,3,7) = 42 </p>

47 <h3>Explanation</h3>

46 <h3>Explanation</h3>

48 <p>LHS is equal to the RHS, the statement is true.</p>

47 <p>LHS is equal to the RHS, the statement is true.</p>

49 <p>Well explained 👍</p>

48 <p>Well explained 👍</p>

50 <h3>Problem 2</h3>

49 <h3>Problem 2</h3>

51 <p>a=2, b=3, c=7. Verify using → LCM(a,b,c) = LCM(LCM(a,b),c)</p>

50 <p>a=2, b=3, c=7. Verify using → LCM(a,b,c) = LCM(LCM(a,b),c)</p>

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

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

53 <p>LCM of 2,3;</p>

52 <p>LCM of 2,3;</p>

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

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

55 <p>Prime factorization of 2 = 21</p>

54 <p>Prime factorization of 2 = 21</p>

56 <p>LCM(2,3) = 6 </p>

55 <p>LCM(2,3) = 6 </p>

57 <p>Use the obtained LCM in the below; </p>

56 <p>Use the obtained LCM in the below; </p>

58 <p>LCM of 6,7; </p>

57 <p>LCM of 6,7; </p>

59 <p>Prime factorization of 6 = 21×31</p>

58 <p>Prime factorization of 6 = 21×31</p>

60 <p>Prime factorization of 7 = 71</p>

59 <p>Prime factorization of 7 = 71</p>

61 <p>LCM(6,7) = 42 </p>

60 <p>LCM(6,7) = 42 </p>

62 <h3>Explanation</h3>

61 <h3>Explanation</h3>

63 <p>LCM(2,3,7) =42, it verifies with the given formula. </p>

62 <p>LCM(2,3,7) =42, it verifies with the given formula. </p>

64 <p>Well explained 👍</p>

63 <p>Well explained 👍</p>

65 <h3>Problem 3</h3>

64 <h3>Problem 3</h3>

66 <p>Find x, LCM(3,9,x) = 72</p>

65 <p>Find x, LCM(3,9,x) = 72</p>

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

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

68 <p>We know that the LCM of 3,9 = 9 The prime factorization of 72 = 23×32 The LCM of 3,9 already includes 32, and the factor of x must include 23, which is 8. </p>

67 <p>We know that the LCM of 3,9 = 9 The prime factorization of 72 = 23×32 The LCM of 3,9 already includes 32, and the factor of x must include 23, which is 8. </p>

69 <h3>Explanation</h3>

68 <h3>Explanation</h3>

70 <p>By following the above assumption we assume that the value of x is 8. </p>

69 <p>By following the above assumption we assume that the value of x is 8. </p>

71 <p>Well explained 👍</p>

70 <p>Well explained 👍</p>

72 <h2>FAQs on LCM of 2,3 and 7</h2>

71 <h2>FAQs on LCM of 2,3 and 7</h2>

73 <h3>1.What is the LCM of 2,4 and 7?</h3>

72 <h3>1.What is the LCM of 2,4 and 7?</h3>

74 <p>28 is the smallest number that appears commonly on the list of the numbers 2,4 and 7. LCM (2,4,7) = 28 </p>

73 <p>28 is the smallest number that appears commonly on the list of the numbers 2,4 and 7. LCM (2,4,7) = 28 </p>

75 <h3>2. What is the GCF of 3, 9, and 12?</h3>

74 <h3>2. What is the GCF of 3, 9, and 12?</h3>

76 <p>Factors of 3 = 1, 3 </p>

75 <p>Factors of 3 = 1, 3 </p>

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

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

78 <p>Factors of 12 = 1, 2, 3, 4, 6</p>

77 <p>Factors of 12 = 1, 2, 3, 4, 6</p>

79 <p>The<a>common factor</a>between the numbers 3, 9, and 12 is 3. The GCF (3,9,12) = 3 </p>

78 <p>The<a>common factor</a>between the numbers 3, 9, and 12 is 3. The GCF (3,9,12) = 3 </p>

80 <h3>3.Find the LCM of 3 and 4.</h3>

79 <h3>3.Find the LCM of 3 and 4.</h3>

81 <p>LCM (3,4) = 12. 12 is the smallest number that appears commonly on the lists of the numbers 3 and 4. </p>

80 <p>LCM (3,4) = 12. 12 is the smallest number that appears commonly on the lists of the numbers 3 and 4. </p>

82 <h3>4.What is the LCM of 9 and 12?</h3>

81 <h3>4.What is the LCM of 9 and 12?</h3>

83 <p>36 is the smallest number that appears commonly on the lists of the numbers 9 and 12. LCM (9,12) = 36 </p>

82 <p>36 is the smallest number that appears commonly on the lists of the numbers 9 and 12. LCM (9,12) = 36 </p>

84 <h3>5. What is the LCM of 4,2 and 8?</h3>

83 <h3>5. What is the LCM of 4,2 and 8?</h3>

85 <p>LCM (4,2,8) = 8. </p>

84 <p>LCM (4,2,8) = 8. </p>

86 <p>8 is the smallest number that appears commonly on the lists of the numbers 2,4 and 8 </p>

85 <p>8 is the smallest number that appears commonly on the lists of the numbers 2,4 and 8 </p>

87 <h2>Important glossaries for the LCM of 2,3 and 7</h2>

86 <h2>Important glossaries for the LCM of 2,3 and 7</h2>

88 <ul><li><strong>Multiple -</strong>product of a number and a natural integer </li>

87 <ul><li><strong>Multiple -</strong>product of a number and a natural integer </li>

89 </ul><ul><li><strong>Prime factor -</strong>number one gets after prime factorization any given number </li>

88 </ul><ul><li><strong>Prime factor -</strong>number one gets after prime factorization any given number </li>

90 </ul><ul><li><strong>Prime factorization -</strong>the process of breaking the number into its prime factors. </li>

89 </ul><ul><li><strong>Prime factorization -</strong>the process of breaking the number into its prime factors. </li>

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

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

92 <p>▶</p>

91 <p>▶</p>

93 <h2>Hiralee Lalitkumar Makwana</h2>

92 <h2>Hiralee Lalitkumar Makwana</h2>

94 <h3>About the Author</h3>

93 <h3>About the Author</h3>

95 <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>

94 <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>

96 <h3>Fun Fact</h3>

95 <h3>Fun Fact</h3>

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

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