What Is The Least Common Multiple Of 7 And 8?

LCM of 7 and 8 How to Find LCM of 7, 8? from www.cuemath.com

Introduction

When it comes to mathematics, there are various concepts and formulas that one needs to understand. One of these concepts is the least common multiple or LCM. It is a fundamental concept that is used in various mathematical operations. In this article, we will discuss what the least common multiple of 7 and 8 is, and how to calculate it.

Understanding Multiples

Before we dive into the concept of the least common multiple, let's first understand what multiples are. In mathematics, multiples are the result of multiplying a given number by a whole number. For instance, the multiples of 7 are 7, 14, 21, 28, and so on.

What is the Least Common Multiple?

The least common multiple, also known as the LCM, is the smallest multiple that two or more numbers have in common. For instance, the LCM of 2 and 3 is 6, because 6 is the smallest multiple that both 2 and 3 share.

Calculating the LCM of 7 and 8

To calculate the LCM of 7 and 8, we need to find the smallest multiple that both numbers share. We can start by listing the multiples of each number. Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70... Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80... We can see that both 56 and 112 are common multiples of 7 and 8. However, 56 is the smallest multiple that both numbers share. Therefore, the LCM of 7 and 8 is 56.

Formula for Finding the LCM

While listing the multiples of each number is one way to find the LCM, there is a faster and more efficient way to calculate it. This can be done by using the prime factorization method. To use this method, we need to: 1. Write each number as a product of its prime factors. 2. Identify the common prime factors of both numbers. 3. Multiply the common prime factors and any remaining factors to get the LCM. For example, let's find the LCM of 12 and 20 using the prime factorization method. Prime factors of 12: 2 x 2 x 3 Prime factors of 20: 2 x 2 x 5 Common prime factors: 2 x 2 = 4 Remaining factors: 3 and 5 LCM = 4 x 3 x 5 = 60

Conclusion

In conclusion, the least common multiple is the smallest multiple that two or more numbers share. To calculate the LCM of two numbers, we can either list the multiples of each number or use the prime factorization method. While the LCM may seem like a simple concept, it is an important one in mathematics and is used in various operations such as adding and subtracting fractions.