What Are The Least Common Multiples Of 9 And 12?

LCM of 9 and 12 How to Find LCM of 9, 12? from www.cuemath.com

Introduction

As a professional teacher, I understand that students often find it challenging to understand the concept of least common multiples. In this article, we will discuss what least common multiples are and how to find them for the numbers 9 and 12.

What are Multiples?

Before we move on to the concept of least common multiples, it is essential to understand the term multiples. Multiples are the numbers that can be divided into a given number without leaving any remainder. For example, the multiples of 6 are 6, 12, 18, 24, and so on.

What is the Least Common Multiple?

The least common multiple (LCM) of two or more numbers is the smallest number that is a multiple of all the given numbers. For example, the LCM of 2 and 3 is 6, as 6 is the smallest number that is a multiple of both 2 and 3.

Finding the LCM of 9 and 12

To find the LCM of 9 and 12, we need to list down their multiples and find the smallest number that is common in both the lists. Multiples of 9 are: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, 117, 126, 135, 144, 153, 162, 171, 180, 189, 198, 207, 216, 225, and so on. Multiples of 12 are: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180, 192, 204, 216, 228, 240, and so on.

Method 1: Listing Method

One way to find the LCM of 9 and 12 is to list down their multiples until we find the smallest number that is common in both the lists. From the above lists, we can see that the smallest number that is common in both lists is 36. Therefore, the LCM of 9 and 12 is 36.

Method 2: Prime Factorization Method

Another way to find the LCM of 9 and 12 is to use the prime factorization method. To use this method, we need to find the prime factors of both 9 and 12. The prime factors of 9 are 3 x 3, and the prime factors of 12 are 2 x 2 x 3. Then, we need to write down the prime factors of both numbers in a vertical line, and the LCM will be the product of all the prime factors with the highest power. 3 3 2 2 3 ---------------- 2 3 3 x 2 = 6 From the above calculation, we can see that the LCM of 9 and 12 is 36, which is the same as the answer we got using the listing method.

Conclusion

In conclusion, the least common multiple (LCM) of 9 and 12 is 36. We can find the LCM of any two or more numbers by listing down their multiples or using the prime factorization method. Understanding the concept of LCM is essential for solving various mathematical problems, and I hope this article has helped you understand it better.