Explanation And Solution For "Least Common Multiple 6 And 15"

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

Introduction

In math, finding the least common multiple (LCM) of two numbers is a common task. The LCM is the smallest number that is a multiple of two or more numbers. In this article, we will discuss how to find the LCM of 6 and 15.

What is the LCM?

The LCM of two numbers is the smallest number that both numbers can divide into evenly. In other words, it is the smallest common multiple of the two numbers. For example, the LCM of 6 and 15 is 30, because 30 is the smallest number that both 6 and 15 can divide into evenly.

Method 1: Listing Multiples

One way to find the LCM of two numbers is to list their multiples and find the smallest multiple that they have in common. To do this, we can start by listing the multiples of 6 and 15: Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, ... Multiples of 15: 15, 30, 45, 60, 75, 90, 105, ... We can see that the smallest multiple that they have in common is 30, so the LCM of 6 and 15 is 30.

Method 2: Prime Factorization

Another way to find the LCM of two numbers is to use their prime factorization. To do this, we can find the prime factors of each number and then multiply the highest power of each factor together. Prime factors of 6: 2 x 3 Prime factors of 15: 3 x 5 We can see that both numbers have a factor of 3. To find the LCM, we multiply the highest power of each factor together: 2 x 3 x 5 = 30. Therefore, the LCM of 6 and 15 is 30.

Conclusion

In conclusion, the LCM of 6 and 15 is 30. We can find the LCM by listing multiples or by using prime factorization. The method you choose may depend on the numbers you are working with and your personal preference.