What Is The Lcm Of 10 And 6?

LCM of 6 and 10 How to Find LCM of 6, 10? from www.cuemath.com

Introduction

The Least Common Multiple (LCM) is a mathematical concept that is used to find the smallest number that is a multiple of two or more given numbers. It is used in various mathematical operations, including simplifying fractions, finding equivalent fractions, and solving equations. In this article, we will discuss the LCM of 10 and 6.

What is a multiple?

A multiple is a product of a number and an integer. For example, the multiples of 10 are 10, 20, 30, 40, and so on. The multiples of 6 are 6, 12, 18, 24, and so on.

What is the LCM?

The LCM of two or more numbers is the smallest number that is a multiple of all the given numbers. For example, the LCM of 10 and 6 is 30 because it is the smallest number that is a multiple of both 10 and 6.

How to find the LCM?

There are different methods to find the LCM of two or more numbers. One method is to list the multiples of each number and find the smallest common multiple. Another method is to use the prime factorization of each number.

Method 1: Listing multiples

To find the LCM of 10 and 6 using this method, we can list the multiples of each number until we find a common multiple. Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, ... Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, ... The smallest common multiple is 30, so the LCM of 10 and 6 is 30.

Method 2: Prime factorization

To find the LCM of 10 and 6 using this method, we can first find the prime factorization of each number. Prime factorization of 10: 2 x 5 Prime factorization of 6: 2 x 3 Then, we can find the highest power of each prime factor that appears in either factorization. Highest power of 2: 2 Highest power of 3: 1 Highest power of 5: 1 The LCM is the product of the prime factors raised to their highest powers, which gives us: LCM of 10 and 6: 2² x 3¹ x 5¹ = 30

Conclusion

In conclusion, the LCM of 10 and 6 is 30. We can find the LCM using different methods, such as listing multiples or using prime factorization. The LCM is a useful concept in mathematics and is used in various applications.