Understanding The Least Common Factor Of 8 And 9

LCM of 8, 9 and 12 How to Find LCM of 8, 9, 12? from www.cuemath.com

Introduction

When it comes to mathematics, finding the least common factor or multiple of two numbers is a common task. In this article, we will focus on finding the least common factor of 8 and 9.

What is a Factor?

Before we proceed, let us first define what a factor is. In mathematics, a factor is a number that divides another number without leaving a remainder. For example, the factors of 8 are 1, 2, 4, and 8 because these numbers divide 8 without leaving a remainder.

What is the Least Common Factor?

The least common factor (LCF) or least common multiple (LCM) of two numbers is the smallest number that is a multiple of both numbers. In other words, it is the smallest number that both 8 and 9 can divide.

How to Find the LCF of 8 and 9?

To find the LCF of 8 and 9, we need to list down the multiples of each number and find the smallest number that appears in both lists. Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, … Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, … From the lists above, we can see that the smallest number that appears in both lists is 72. Therefore, the LCF of 8 and 9 is 72.

Why is 72 the LCF of 8 and 9?

To understand why 72 is the LCF of 8 and 9, we need to know that 72 is a multiple of 8 and 9. In fact, 72 is the smallest common multiple of 8 and 9.

What is a Multiple?

Similar to factors, multiples are also important in mathematics. A multiple is a number that is the product of another number and an integer. For example, the multiples of 8 are 8, 16, 24, 32, 40, 48, and so on because these numbers are the product of 8 and an integer.

How to Check if a Number is a Multiple of Another Number?

To check if a number is a multiple of another number, we simply divide the first number by the second number. If the division results in a whole number, then the first number is a multiple of the second number. For example, 72 divided by 8 is 9, which is a whole number. Therefore, 72 is a multiple of 8.

Conclusion

Finding the LCF of two numbers can be a simple task if we know how to list down the multiples of each number and find the smallest number that appears in both lists. In the case of 8 and 9, the LCF is 72 because it is the smallest number that both 8 and 9 can divide.