Solution: The LCM of 52 and 22 is 572
Methods
How to find the LCM of 52 and 22 using Prime Factorization
One way to find the LCM of 52 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 52?
What are the Factors of 22?
Here is the prime factorization of 52:
2
2
×
1
3
1
2^2 × 13^1
2 2 × 1 3 1
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: 2, 13, 11
2
2
×
1
1
1
×
1
3
1
=
572
2^2 × 11^1 × 13^1 = 572
2 2 × 1 1 1 × 1 3 1 = 572
Through this we see that the LCM of 52 and 22 is 572.
How to Find the LCM of 52 and 22 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 52 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, 52 and 22:
What are the Multiples of 52?
What are the Multiples of 22?
Let’s take a look at the first 10 multiples for each of these numbers, 52 and 22:
First 10 Multiples of 52: 52, 104, 156, 208, 260, 312, 364, 416, 468, 520
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 52 and 22 are 572, 1144, 1716. Because 572 is the smallest, it is the least common multiple.
The LCM of 52 and 22 is 572.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 137 and 18?
What is the LCM of 146 and 20?
What is the LCM of 150 and 31?
What is the LCM of 13 and 69?
What is the LCM of 1 and 61?