Solution: The LCM of 8 and 9 is 72
Methods
How to find the LCM of 8 and 9 using Prime Factorization
One way to find the LCM of 8 and 9 is to start by comparing the prime factorization of each number. To find the prime factorization, you can follow the instructions for each number here:
What are the Factors of 8?
What are the Factors of 9?
Here is the prime factorization of 8:
2
3
2^3
2 3
And this is the prime factorization of 9:
3
2
3^2
3 2
When you compare the prime factorization of these two numbers, you want to look for the highest power that each prime factor is raised to. In this case, there are these prime factors to consider: 2, 3
2
3
×
3
2
=
72
2^3 × 3^2 = 72
2 3 × 3 2 = 72
Through this we see that the LCM of 8 and 9 is 72.
How to Find the LCM of 8 and 9 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 8 and 9 is to begin to list a few multiples for each number. If you need a refresher on how to find the multiples of these numbers, you can see the walkthroughs in the links below for each number.
Let’s take a look at the multiples for each of these numbers, 8 and 9:
What are the Multiples of 8?
What are the Multiples of 9?
Let’s take a look at the first 10 multiples for each of these numbers, 8 and 9:
First 10 Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80
First 10 Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90
You can continue to list out the multiples of these numbers as long as needed to find a match. Once you do find a match, or several matches, the smallest of these matches would be the Least Common Multiple. For instance, the first matching multiple(s) of 8 and 9 are 72, 144, 216. Because 72 is the smallest, it is the least common multiple.
The LCM of 8 and 9 is 72.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 33 and 101?
What is the LCM of 64 and 28?
What is the LCM of 113 and 102?
What is the LCM of 24 and 18?
What is the LCM of 73 and 105?