Explaining And Solving 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

The Least Common Multiple (LCM) is a mathematical concept that is essential in various fields, such as engineering, science, and finance. It is a critical tool for solving problems involving fractions, ratios, and proportions. In this article, we will discuss the LCM of 7 and 8 and how to determine it.

What is LCM?

LCM is the smallest positive integer that is a multiple of two or more given numbers. In other words, it is the smallest number that both 7 and 8 can divide into without a remainder.

How to Find the LCM of 7 and 8?

There are several methods for finding the LCM of two numbers, but we will discuss the most straightforward method, which is the prime factorization method.

Step 1: Prime Factorization

Prime factorization is the process of finding the prime factors of a number. To find the LCM of 7 and 8, we need to factorize both numbers into their primes. 7 is a prime number, so its prime factorization is 7. 8 can be factorized into 2 x 2 x 2, which is written as 2^3.

Step 2: Multiplying the Prime Factors

The next step is to multiply all the prime factors that appear in either number. Multiplying 7 and 2^3 gives us 56. Therefore, 56 is the LCM of 7 and 8.

Conclusion

In summary, the LCM of 7 and 8 is 56. To determine the LCM of any two numbers, we need to factorize them into their primes and then multiply all the primes that appear in either number. The LCM is an important concept in mathematics that has practical applications in various fields.