Understanding The Least Common Multiple Of 3 And 12

Least Common Multiples (LCM) One PagerAccuTeach from www.accuteach.com

Introduction

As a professional teacher, one of the concepts that we need to teach our students is the Least Common Multiple (LCM). LCM is the smallest multiple that two or more numbers have in common. In this article, we will be discussing the LCM of 3 and 12.

Prime Factors

To find the LCM of 3 and 12, we need to find the prime factors of each number. Prime factors are the factors of a number that are only divisible by that number and 1. The prime factors of 3 are 3 and 1. The prime factors of 12 are 2, 2, 3, and 1.

Listing the Multiples

After finding the prime factors, we need to list down the multiples of the numbers. The multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, and so on. The multiples of 12 are 12, 24, 36, 48, 60, 72, and so on.

Finding the Common Multiples

From the list of multiples, we can see that the numbers 12 and 24 are common multiples of 3 and 12. However, we need to find the smallest common multiple, which is the LCM.

Comparing the Common Multiples

To compare the common multiples, we need to find the smallest number that can be divided by both 3 and 12 without leaving a remainder. We can use the multiples 12 and 24 to find the LCM.

Dividing the Multiples

To find the LCM, we can divide the multiples by the GCF (Greatest Common Factor) of 3 and 12, which is 3. 12 divided by 3 is equal to 4 and 24 divided by 3 is equal to 8.

Multiplying the Quotients

After dividing the multiples, we can multiply the quotients to find the LCM. The LCM of 3 and 12 is equal to 4 multiplied by 8, which is equal to 32.

Conclusion

In conclusion, the LCM of 3 and 12 is 32. As teachers, it is important to explain the concept of LCM to our students using different methods and examples. By understanding LCM, our students can easily solve problems that involve finding the common multiples of two or more numbers.