Solution: The LCM of 138 and 52 is 3588
Methods
How to find the LCM of 138 and 52 using Prime Factorization
One way to find the LCM of 138 and 52 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 138?
What are the Factors of 52?
Here is the prime factorization of 138:
2
1
×
3
1
×
2
3
1
2^1 × 3^1 × 23^1
2 1 × 3 1 × 2 3 1
And this is the prime factorization of 52:
2
2
×
1
3
1
2^2 × 13^1
2 2 × 1 3 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, 3, 23, 13
2
2
×
3
1
×
1
3
1
×
2
3
1
=
3588
2^2 × 3^1 × 13^1 × 23^1 = 3588
2 2 × 3 1 × 1 3 1 × 2 3 1 = 3588
Through this we see that the LCM of 138 and 52 is 3588.
How to Find the LCM of 138 and 52 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 138 and 52 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, 138 and 52:
What are the Multiples of 138?
What are the Multiples of 52?
Let’s take a look at the first 10 multiples for each of these numbers, 138 and 52:
First 10 Multiples of 138: 138, 276, 414, 552, 690, 828, 966, 1104, 1242, 1380
First 10 Multiples of 52: 52, 104, 156, 208, 260, 312, 364, 416, 468, 520
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 138 and 52 are 3588, 7176, 10764. Because 3588 is the smallest, it is the least common multiple.
The LCM of 138 and 52 is 3588.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 71 and 22?
What is the LCM of 109 and 43?
What is the LCM of 87 and 150?
What is the LCM of 139 and 148?
What is the LCM of 34 and 91?