Understanding The Least Common Multiple Of 8 And 9

LCM of 8 and 9 How to Find LCM of 8, 9? from www.cuemath.com

Introduction

In mathematics, the least common multiple (LCM) is a concept used to determine the smallest multiple that two or more numbers have in common. When dealing with numbers, it is essential to understand the LCM since it is used in various mathematical operations. In this article, we will explore the LCM of 8 and 9 and provide a detailed explanation of how to calculate it.

What is the LCM?

The LCM is the smallest number that is a multiple of two or more numbers. For example, the LCM of 4 and 6 is 12 because 12 is a multiple of both 4 and 6. The concept of LCM is used in various mathematical operations such as adding and subtracting fractions, simplifying fractions, and solving equations.

Calculating the LCM of 8 and 9

To calculate the LCM of 8 and 9, we need to find the smallest number that is a multiple of both numbers. We can start by listing the multiples of each number and finding the smallest number that they have in common. Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120 Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, 117, 126 From the above list, we can see that the smallest number that is a multiple of both 8 and 9 is 72. Therefore, the LCM of 8 and 9 is 72.

Why is 72 the LCM?

To understand why 72 is the LCM of 8 and 9, we need to look at the factors of each number. Factors are the numbers that can be multiplied together to get the original number. For example, the factors of 8 are 1, 2, 4, and 8, while the factors of 9 are 1, 3, and 9. When we list the multiples of 8 and 9, we can see that they have common factors of 1, 2, 3, 4, 6, 8, and 9. The smallest number that has all these factors is 72, which is why it is the LCM of 8 and 9.

Applications of LCM

The concept of LCM is used in various mathematical operations, such as adding and subtracting fractions. When adding or subtracting fractions with different denominators, we need to find the LCM of the denominators to make them the same. For example, if we want to add 3/8 and 2/9, we need to find the LCM of 8 and 9, which is 72. We then convert the fractions to have a common denominator of 72 and add them.

Conclusion

In conclusion, the LCM of 8 and 9 is 72. The LCM is the smallest number that two or more numbers have in common. We can find the LCM by listing the multiples of each number and finding the smallest number they have in common. The concept of LCM is used in various mathematical operations, such as adding and subtracting fractions. Understanding the LCM is essential in mathematics, and it is a concept that students should master.