Understanding Lcm For 15 And 9

LCM of 9 and 15 How to Find LCM of 9, 15? from www.cuemath.com

Introduction

LCM stands for Least Common Multiple. It is one of the fundamental concepts of mathematics that is essential in solving different arithmetic problems. In this article, we will discuss LCM for 15 and 9.

What is LCM?

LCM is the smallest number that is a multiple of two or more numbers. It is also known as the Lowest Common Multiple. The LCM of two numbers is the smallest number that is divisible by both these numbers.

How to find LCM?

To find the LCM of two numbers, we need to find the multiples of each number and then look for the smallest multiple that is common to both numbers. The process of finding LCM involves prime factorization, and it is a common method used to find LCM for any two numbers.

Prime Factorization

Prime factorization is the process of breaking down a number into its prime factors. To find the LCM of 15 and 9, we need to factorize these two numbers. 15 = 3 x 5 9 = 3 x 3

Listing Multiples

After finding the prime factors of the two numbers, we need to list down their multiples. Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, 135, 150... Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90...

Finding LCM

We can see that the first common multiple for 15 and 9 is 45. Therefore, the LCM of 15 and 9 is 45. We can also verify this by checking the other multiples of 45 and see if they are divisible by both 15 and 9.

Conclusion

In conclusion, LCM is a fundamental concept of mathematics that is essential to solve various arithmetic problems. To find the LCM of two numbers, we need to factorize the numbers, list down their multiples, and find the smallest common multiple. In the case of 15 and 9, the LCM is 45.

Practice Problem

Find the LCM of 12 and 15.

Solution

12 = 2 x 2 x 3 15 = 3 x 5 Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120... Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, 135, 150... The first common multiple is 60. Therefore, the LCM of 12 and 15 is 60.