Solution: The LCM of 54 and 52 is 1404
Methods
How to find the LCM of 54 and 52 using Prime Factorization
One way to find the LCM of 54 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 54?
What are the Factors of 52?
Here is the prime factorization of 54:
2
1
×
3
3
2^1 × 3^3
2 1 × 3 3
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, 13
2
2
×
3
3
×
1
3
1
=
1404
2^2 × 3^3 × 13^1 = 1404
2 2 × 3 3 × 1 3 1 = 1404
Through this we see that the LCM of 54 and 52 is 1404.
How to Find the LCM of 54 and 52 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 54 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, 54 and 52:
What are the Multiples of 54?
What are the Multiples of 52?
Let’s take a look at the first 10 multiples for each of these numbers, 54 and 52:
First 10 Multiples of 54: 54, 108, 162, 216, 270, 324, 378, 432, 486, 540
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 54 and 52 are 1404, 2808, 4212. Because 1404 is the smallest, it is the least common multiple.
The LCM of 54 and 52 is 1404.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 129 and 140?
What is the LCM of 65 and 125?
What is the LCM of 144 and 26?
What is the LCM of 149 and 124?
What is the LCM of 55 and 19?