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

3 <p>LCM of any two numbers is the least common multiple of two numbers. In our daily life, LCM is used for scheduling events, and distributing any items among others. In this topic, we will learn more about LCMs 3, 8, and 12.</p>

4 <h2>What is the LCM of 3, 8 and 12</h2>

5 <p>The<a>common multiple</a><a>of</a>3, 8, and 12 is 24 Here, we will learn about the LCM of 3<a>numbers</a>. Children learn about LCM at younger ages. Here, we will discuss the methods used for finding out LCM. </p>

6 <h2>How to find the LCM of 3,8 and 12</h2>

7 <p>Out of many methods,<a>prime factorization</a>method is widely used for its easy approach. Here, we will learn about other methods as well. A few commonly used methods are as follows - </p>

8 <ol><li>Listing Of Multiples</li>

9 <li>Prime Factorization</li>

10 <li>Division Method </li>

11 </ol><h3>LCM of 3, 8, and 12 Using Listing the Multiples</h3>

12 <p>Listing<a>multiples</a>can be a tedious method for finding the LCM. Here, the listing of multiples for all these 3 numbers is noted - </p>

13 <ul><li>Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24…</li>

14 <li>Multiples of 8: 8, 16, 24…</li>

15 <li>Multiples of 12: 12, 24…</li>

16 </ul><p>Then we can see that out of 3, 8, and 12, 24 is the smallest common number that is present in them. So we see that 24 is the LCM of 3, 8, and 12. </p>

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19 <h3>LCM of 3, 8, and 12 Using Prime Factorization</h3>

18 <h3>LCM of 3, 8, and 12 Using Prime Factorization</h3>

20 <p>The<a>product</a>of the highest<a>power</a>of prime<a>factors</a>of 3, 8, and 12 is the LCM of these numbers. So let us look at it step by step to understand it better.</p>

19 <p>The<a>product</a>of the highest<a>power</a>of prime<a>factors</a>of 3, 8, and 12 is the LCM of these numbers. So let us look at it step by step to understand it better.</p>

21 <p>Breaking the given numbers into their prime factors</p>

20 <p>Breaking the given numbers into their prime factors</p>

22 <p>Prime factorization of 3 = 31 Prime factorization of 8 =23 Prime factorization of 12 = 22 × 31 </p>

21 <p>Prime factorization of 3 = 31 Prime factorization of 8 =23 Prime factorization of 12 = 22 × 31 </p>

23 <p>Multiplying the highest power of prime factors: 23 × 31 → 8 × 3 = 24 LCM of 3, 8, and 12 is 24.</p>

22 <p>Multiplying the highest power of prime factors: 23 × 31 → 8 × 3 = 24 LCM of 3, 8, and 12 is 24.</p>

24 <h3>LCM of 3, 8, and 12 Using Division Method</h3>

23 <h3>LCM of 3, 8, and 12 Using Division Method</h3>

25 <p>In this method, we will be dividing the given numbers with the common prime factors until all numbers are reduced to 1. Let us look at this step by step and make it easy for the children to learn it.</p>

24 <p>In this method, we will be dividing the given numbers with the common prime factors until all numbers are reduced to 1. Let us look at this step by step and make it easy for the children to learn it.</p>

26 <p><strong>Step 1:</strong>Arrange the number in a<a>sequence</a>, divisors, and the numbers are on the left and right sides respectively.</p>

25 <p><strong>Step 1:</strong>Arrange the number in a<a>sequence</a>, divisors, and the numbers are on the left and right sides respectively.</p>

27 <p><strong>Step 2:</strong>For finding the<a>divisor</a>, it is always the smallest common prime factor. Here, the smallest common prime factor is 2. Dividing 3, 8, and 12 by 2. The result is 3, 4, and 6. </p>

26 <p><strong>Step 2:</strong>For finding the<a>divisor</a>, it is always the smallest common prime factor. Here, the smallest common prime factor is 2. Dividing 3, 8, and 12 by 2. The result is 3, 4, and 6. </p>

28 <p><strong>Step 3:</strong>As 4 and 6 are divisible by 2, again the divisor is 2. Dividing 3, 4, and 6 by 2. Now the<a>remainder</a>is 3, 2, and 3.</p>

27 <p><strong>Step 3:</strong>As 4 and 6 are divisible by 2, again the divisor is 2. Dividing 3, 4, and 6 by 2. Now the<a>remainder</a>is 3, 2, and 3.</p>

29 <p><strong>Step 4:</strong>Continue dividing the numbers with the smallest<a>prime number</a>until all numbers are reduced to 1.</p>

28 <p><strong>Step 4:</strong>Continue dividing the numbers with the smallest<a>prime number</a>until all numbers are reduced to 1.</p>

30 <p>The divisors are 2, 2, 2, 3. LCM of 3, 8, and 12 is the product of divisors.</p>

29 <p>The divisors are 2, 2, 2, 3. LCM of 3, 8, and 12 is the product of divisors.</p>

31 <p>Hence, the LCM of (3, 8, and 12) = 2 × 2 × 2 × 3 = 24 </p>

30 <p>Hence, the LCM of (3, 8, and 12) = 2 × 2 × 2 × 3 = 24 </p>

32 <h2>Common Mistakes and How to Avoid Them in LCM of 3, 8, and 12.</h2>

31 <h2>Common Mistakes and How to Avoid Them in LCM of 3, 8, and 12.</h2>

33 <p>There are some common mistakes that are made by children while solving a problem on LCM. Let us look at some of these mistakes and how we can help children to avoid these mistakes.</p>

32 <p>There are some common mistakes that are made by children while solving a problem on LCM. Let us look at some of these mistakes and how we can help children to avoid these mistakes.</p>

34 <h3>Problem 1</h3>

33 <h3>Problem 1</h3>

35 <p>Three students exercise every 3, 8, and 12 days, respectively. If they all exercise today, when will they exercise together next?</p>

34 <p>Three students exercise every 3, 8, and 12 days, respectively. If they all exercise today, when will they exercise together next?</p>

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

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

37 <p>List the multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24 List the multiples of 8: 8, 16, 24 List the multiples of 12: 12, 24</p>

36 <p>List the multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24 List the multiples of 8: 8, 16, 24 List the multiples of 12: 12, 24</p>

38 <p>So, we get the smallest common multiple in both lists as 24</p>

37 <p>So, we get the smallest common multiple in both lists as 24</p>

39 <p>So the LCM of 3,8 and 12 is 24 (which is 24 days) </p>

38 <p>So the LCM of 3,8 and 12 is 24 (which is 24 days) </p>

40 <h3>Explanation</h3>

39 <h3>Explanation</h3>

41 <p> So, they will exercise together again every 24 days. </p>

40 <p> So, they will exercise together again every 24 days. </p>

42 <p>Well explained 👍</p>

41 <p>Well explained 👍</p>

43 <h3>Problem 2</h3>

42 <h3>Problem 2</h3>

44 <p>Three buses on different routes arrive at a stop every 3 minutes,8 minutes, and 12 minutes. If they all arrive together now, how many will they arrive together again?</p>

43 <p>Three buses on different routes arrive at a stop every 3 minutes,8 minutes, and 12 minutes. If they all arrive together now, how many will they arrive together again?</p>

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

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

46 <p>By finding the LCM of 3, 8, and 12 we can find when all the buses come together</p>

45 <p>By finding the LCM of 3, 8, and 12 we can find when all the buses come together</p>

47 <p>Prime factorization of 3 = 3 Prime factorization of 8 = 23 Prime factorization of 12 = 22 × 3</p>

46 <p>Prime factorization of 3 = 3 Prime factorization of 8 = 23 Prime factorization of 12 = 22 × 3</p>

48 <p>LCM (3, 8, 12) = 23 × 3 = 8 ×3 = 24</p>

47 <p>LCM (3, 8, 12) = 23 × 3 = 8 ×3 = 24</p>

49 <p>Therefore, the buses come together every 24 minutes. </p>

48 <p>Therefore, the buses come together every 24 minutes. </p>

50 <h3>Explanation</h3>

49 <h3>Explanation</h3>

51 <p>To find when all the buses come together we find the LCM of 3, 8, and 12. The LCM of 3, 8, and 24 is 24 minutes. </p>

50 <p>To find when all the buses come together we find the LCM of 3, 8, and 12. The LCM of 3, 8, and 24 is 24 minutes. </p>

52 <p>Well explained 👍</p>

51 <p>Well explained 👍</p>

53 <h3>Problem 3</h3>

52 <h3>Problem 3</h3>

54 <p>am has his math class every 3 days, drawing class every 8 days, and swimming class every 12 days. Then find on which day he has all the classes together.</p>

53 <p>am has his math class every 3 days, drawing class every 8 days, and swimming class every 12 days. Then find on which day he has all the classes together.</p>

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

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

56 <p> To find when Sam has all the classes together we find the LCM of 3, 8, and 12.</p>

55 <p> To find when Sam has all the classes together we find the LCM of 3, 8, and 12.</p>

57 <p>Prime factorization of 3 = 3 Prime factorization of 8 = 2 Prime factorization of 12 = 22 × 3</p>

56 <p>Prime factorization of 3 = 3 Prime factorization of 8 = 2 Prime factorization of 12 = 22 × 3</p>

58 <p>Multiplying all the highest power of prime factors = 23 × 31 = 8 × 3 =24</p>

57 <p>Multiplying all the highest power of prime factors = 23 × 31 = 8 × 3 =24</p>

59 <p>Hence, on every 24th day Sam has all the classes together </p>

58 <p>Hence, on every 24th day Sam has all the classes together </p>

60 <h3>Explanation</h3>

59 <h3>Explanation</h3>

61 <p>To predict the recurring event, we find the LCM </p>

60 <p>To predict the recurring event, we find the LCM </p>

62 <p>Well explained 👍</p>

61 <p>Well explained 👍</p>

63 <h2>FAQ on LCM of 3, 8, and 12</h2>

62 <h2>FAQ on LCM of 3, 8, and 12</h2>

64 <h3>1.What is the LCM of 3, 12, and 18?</h3>

63 <h3>1.What is the LCM of 3, 12, and 18?</h3>

65 <p>The LCM of 3, 12, and 18 is 36.</p>

64 <p>The LCM of 3, 12, and 18 is 36.</p>

66 <h3>2.What is the LCM of 4, 8 and 12?</h3>

65 <h3>2.What is the LCM of 4, 8 and 12?</h3>

67 <p>The Least common multiple of 4, 8, and 12 is 24 </p>

66 <p>The Least common multiple of 4, 8, and 12 is 24 </p>

68 <h3>3.What is the LCM of 3,4 and 12?</h3>

67 <h3>3.What is the LCM of 3,4 and 12?</h3>

69 <p> The LCM of 3,4 and 12 is 12 To find the LCM, write the multiple of 3,4 and 12. Then choose the smallest multiple that can be exactly divisible by 3, 4, and 12. </p>

68 <p> The LCM of 3,4 and 12 is 12 To find the LCM, write the multiple of 3,4 and 12. Then choose the smallest multiple that can be exactly divisible by 3, 4, and 12. </p>

70 <h3>4.What is the LCM of 18,8 and 12?</h3>

69 <h3>4.What is the LCM of 18,8 and 12?</h3>

71 <h3>5.What is the LCM of 3 and 8?</h3>

70 <h3>5.What is the LCM of 3 and 8?</h3>

72 <p> The<a>term</a>LCM is“ Least Common Multiples.” The smallest<a>integer</a>that divides the numbers, with no numbers left behind. So the LCM of 3, and 8 is 24. </p>

71 <p> The<a>term</a>LCM is“ Least Common Multiples.” The smallest<a>integer</a>that divides the numbers, with no numbers left behind. So the LCM of 3, and 8 is 24. </p>

73 <h2>Important Glossaries of LCM 3,8 and 12</h2>

72 <h2>Important Glossaries of LCM 3,8 and 12</h2>

74 <ul><li><strong>Factor:</strong>A number that will divide two or more numbers, leaving no remainder. For 18 and 24 we have 6 as a common factor, it means both 18 and 24 can be divisible by 6.</li>

73 <ul><li><strong>Factor:</strong>A number that will divide two or more numbers, leaving no remainder. For 18 and 24 we have 6 as a common factor, it means both 18 and 24 can be divisible by 6.</li>

75 </ul><ul><li><strong>Prime Factorization:</strong>When a number can be represented as the factors of prime numbers, it is called prime factorization. The prime factorization of 18 for example is 2×3×3.</li>

74 </ul><ul><li><strong>Prime Factorization:</strong>When a number can be represented as the factors of prime numbers, it is called prime factorization. The prime factorization of 18 for example is 2×3×3.</li>

76 </ul><ul><li><strong>Greatest Common Factor (GCF):</strong>GCF is the greatest factor that is common in the given numbers. For example, the GCF of 5, 10, and 15 is 5. Because the common factors of 5 and 10 are 1 and 5.</li>

75 </ul><ul><li><strong>Greatest Common Factor (GCF):</strong>GCF is the greatest factor that is common in the given numbers. For example, the GCF of 5, 10, and 15 is 5. Because the common factors of 5 and 10 are 1 and 5.</li>

77 </ul><ul><li><strong>Division Method:</strong>In the division method, the numbers are divided by the smallest common prime factor till the numbers are reduced to 1. </li>

76 </ul><ul><li><strong>Division Method:</strong>In the division method, the numbers are divided by the smallest common prime factor till the numbers are reduced to 1. </li>

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

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

79 <p>▶</p>

78 <p>▶</p>

80 <h2>Hiralee Lalitkumar Makwana</h2>

79 <h2>Hiralee Lalitkumar Makwana</h2>

81 <h3>About the Author</h3>

80 <h3>About the Author</h3>

82 <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>

81 <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>

83 <h3>Fun Fact</h3>

82 <h3>Fun Fact</h3>

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

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