Solution: The LCM of 52 and 31 is 1612
Methods
How to find the LCM of 52 and 31 using Prime Factorization
One way to find the LCM of 52 and 31 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 31?
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 31:
3
1
1
31^1
3 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, 31
2
2
×
1
3
1
×
3
1
1
=
1612
2^2 × 13^1 × 31^1 = 1612
2 2 × 1 3 1 × 3 1 1 = 1612
Through this we see that the LCM of 52 and 31 is 1612.
How to Find the LCM of 52 and 31 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 52 and 31 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 31:
What are the Multiples of 52?
What are the Multiples of 31?
Let’s take a look at the first 10 multiples for each of these numbers, 52 and 31:
First 10 Multiples of 52: 52, 104, 156, 208, 260, 312, 364, 416, 468, 520
First 10 Multiples of 31: 31, 62, 93, 124, 155, 186, 217, 248, 279, 310
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 31 are 1612, 3224, 4836. Because 1612 is the smallest, it is the least common multiple.
The LCM of 52 and 31 is 1612.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 20 and 33?
What is the LCM of 28 and 72?
What is the LCM of 58 and 23?
What is the LCM of 7 and 49?
What is the LCM of 30 and 65?