Understanding The Least Common Multiple Of 10 And 8

LCM of 8 and 10 How to Find LCM of 8, 10? from www.cuemath.com

Introduction

In mathematics, the least common multiple (LCM) is a crucial concept used to find the smallest multiple that two or more numbers share. In this article, we will focus on finding the LCM of 10 and 8.

Factors of 10 and 8

Before we can find the LCM of 10 and 8, we need to understand the factors of these two numbers. The factors of 10 are 1, 2, 5, and 10. On the other hand, the factors of 8 are 1, 2, 4, and 8.

Method 1: Listing Multiples

One way to find the LCM of 10 and 8 is by listing their multiples and finding the smallest multiple they have in common. The multiples of 10 are 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, and so on. The multiples of 8 are 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, and so on. From this list, we can see that the smallest multiple that 10 and 8 share is 40. Therefore, the LCM of 10 and 8 is 40.

Method 2: Prime Factorization

Another way to find the LCM of 10 and 8 is by using prime factorization. To use this method, we need to express each number as a product of its prime factors. The prime factors of 10 are 2 and 5, while the prime factors of 8 are 2, 2, and 2. We then take the highest power of each prime factor and multiply them together. In this case, the highest power of 2 is 2^3, and the highest power of 5 is 5^1. Therefore, the LCM of 10 and 8 is 2^3 * 5^1 = 40.

Applications of LCM

The LCM of 10 and 8 has many real-world applications. For example, if we want to find the smallest number of guests we need to invite to ensure that we have enough chairs for everyone, we can use the LCM of the number of chairs per table and the number of chairs per guest. In this case, if each table has 10 chairs, and each guest needs 8 chairs, we need to find the LCM of 10 and 8, which is 40. Therefore, we need to invite 40 guests to ensure that we have enough chairs for everyone.

Conclusion

In conclusion, the LCM of 10 and 8 is 40. We can find the LCM using various methods, including listing multiples and prime factorization. The LCM has many practical applications, including finding the smallest number of guests we need to invite to ensure we have enough chairs for everyone. Understanding the LCM is a fundamental concept in mathematics and is essential for solving many problems in real life.