Solution: The LCM of 9 and 22 is 198
Methods
How to find the LCM of 9 and 22 using Prime Factorization
One way to find the LCM of 9 and 22 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 9?
What are the Factors of 22?
Here is the prime factorization of 9:
3
2
3^2
3 2
And this is the prime factorization of 22:
2
1
×
1
1
1
2^1 × 11^1
2 1 × 1 1 1
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: 3, 2, 11
2
1
×
3
2
×
1
1
1
=
198
2^1 × 3^2 × 11^1 = 198
2 1 × 3 2 × 1 1 1 = 198
Through this we see that the LCM of 9 and 22 is 198.
How to Find the LCM of 9 and 22 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 9 and 22 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, 9 and 22:
What are the Multiples of 9?
What are the Multiples of 22?
Let’s take a look at the first 10 multiples for each of these numbers, 9 and 22:
First 10 Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90
First 10 Multiples of 22: 22, 44, 66, 88, 110, 132, 154, 176, 198, 220
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 9 and 22 are 198, 396, 594. Because 198 is the smallest, it is the least common multiple.
The LCM of 9 and 22 is 198.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 50 and 19?
What is the LCM of 116 and 132?
What is the LCM of 102 and 44?
What is the LCM of 144 and 15?
What is the LCM of 28 and 78?