The Least Common Multiple Of 15 And 6

LCM (Least Common Multiple) How to Find LCM? Examples from www.cuemath.com

Introduction

When we talk about the least common multiple (LCM) of two numbers, we are referring to the smallest number which is a multiple of both of them. In this case, we will be discussing the LCM of 15 and 6.

What is a Multiple?

Before we dive into LCM, let's first define what a multiple is. A multiple is the product of a number and any whole number. For example, the multiples of 6 are 6, 12, 18, 24, 30, and so on.

How to Find the LCM of 15 and 6

To find the LCM of 15 and 6, we need to list out their multiples and find the smallest one they have in common. Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, ... Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, ... From the lists above, we can see that the smallest common multiple of 15 and 6 is 30. Therefore, the LCM of 15 and 6 is 30.

Why is 30 the LCM?

To understand why 30 is the LCM of 15 and 6, we need to look at their prime factors. Prime factors of 15: 3 x 5 Prime factors of 6: 2 x 3 The LCM of 15 and 6 is the product of the highest powers of all the prime factors. In this case, the highest power of 2 is 2, the highest power of 3 is 1, and the highest power of 5 is 1. Therefore, the LCM of 15 and 6 is 2 x 3 x 5, which is 30.

Why is LCM Important?

The LCM is important in many mathematical problems, such as when we need to add or subtract fractions with different denominators. In order to do this, we need to find the LCM of the denominators and then convert the fractions to have the same denominator.

Conclusion

In conclusion, the LCM of 15 and 6 is 30. This is the smallest number that is a multiple of both 15 and 6. Understanding how to find the LCM is important in many mathematical problems and can help simplify calculations.