Solution: The LCM of 22 and 120 is 1320
Methods
How to find the LCM of 22 and 120 using Prime Factorization
One way to find the LCM of 22 and 120 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 22?
What are the Factors of 120?
Here is the prime factorization of 22:
2
1
×
1
1
1
2^1 × 11^1
2 1 × 1 1 1
And this is the prime factorization of 120:
2
3
×
3
1
×
5
1
2^3 × 3^1 × 5^1
2 3 × 3 1 × 5 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: 2, 11, 3, 5
2
3
×
3
1
×
5
1
×
1
1
1
=
1320
2^3 × 3^1 × 5^1 × 11^1 = 1320
2 3 × 3 1 × 5 1 × 1 1 1 = 1320
Through this we see that the LCM of 22 and 120 is 1320.
How to Find the LCM of 22 and 120 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 22 and 120 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, 22 and 120:
What are the Multiples of 22?
What are the Multiples of 120?
Let’s take a look at the first 10 multiples for each of these numbers, 22 and 120:
First 10 Multiples of 22: 22, 44, 66, 88, 110, 132, 154, 176, 198, 220
First 10 Multiples of 120: 120, 240, 360, 480, 600, 720, 840, 960, 1080, 1200
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 22 and 120 are 1320, 2640, 3960. Because 1320 is the smallest, it is the least common multiple.
The LCM of 22 and 120 is 1320.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 28 and 148?
What is the LCM of 10 and 98?
What is the LCM of 53 and 95?
What is the LCM of 40 and 120?
What is the LCM of 128 and 17?