What Is The Lcm Of 8 And 9?

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

Introduction

In mathematics, LCM stands for Least Common Multiple. It is the smallest number that is a multiple of two or more numbers. LCM is widely used in many mathematical problems, especially in fractions, percentages, and ratios. In this article, we will discuss the LCM of 8 and 9.

What are multiples?

Multiples are the numbers obtained by multiplying a number by another number. For example, the multiples of 3 are 3, 6, 9, 12, 15, and so on. Similarly, the multiples of 4 are 4, 8, 12, 16, 20, and so on.

What is the LCM of 8 and 9?

To find the LCM of 8 and 9, we need to list the multiples of each number and find the smallest multiple that is common to both. Let's list the multiples of 8 and 9: Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, and so on. Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, and so on. From the above list, we can see that the smallest multiple that is common to both 8 and 9 is 72. Therefore, the LCM of 8 and 9 is 72.

Why is 72 the LCM of 8 and 9?

To understand why 72 is the LCM of 8 and 9, we need to look at the prime factors of both numbers. Prime factors are the factors of a number that are prime numbers. For example, the prime factors of 12 are 2, 2, and 3. The prime factors of 8 are 2 x 2 x 2, and the prime factors of 9 are 3 x 3. To find the LCM of 8 and 9, we need to take the highest power of each prime factor. In this case, the highest power of 2 is 3, and the highest power of 3 is 2. Therefore, the LCM of 8 and 9 is 2^3 x 3^2, which is equal to 72.

Applications of LCM

LCM is used in many mathematical problems, especially in fractions, percentages, and ratios. For example, to add or subtract fractions with different denominators, we need to find the LCM of the denominators. LCM is also used to simplify fractions and convert fractions to decimals or percentages.

Conclusion

In conclusion, the LCM of 8 and 9 is 72. To find the LCM of two or more numbers, we need to list the multiples of each number and find the smallest multiple that is common to both. LCM is widely used in many mathematical problems and is an important concept in mathematics.