Solution: The LCM of 24 and 52 is 312
Methods
How to find the LCM of 24 and 52 using Prime Factorization
One way to find the LCM of 24 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 24?
What are the Factors of 52?
Here is the prime factorization of 24:
2
3
×
3
1
2^3 × 3^1
2 3 × 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, 13
2
3
×
3
1
×
1
3
1
=
312
2^3 × 3^1 × 13^1 = 312
2 3 × 3 1 × 1 3 1 = 312
Through this we see that the LCM of 24 and 52 is 312.
How to Find the LCM of 24 and 52 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 24 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, 24 and 52:
What are the Multiples of 24?
What are the Multiples of 52?
Let’s take a look at the first 10 multiples for each of these numbers, 24 and 52:
First 10 Multiples of 24: 24, 48, 72, 96, 120, 144, 168, 192, 216, 240
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 24 and 52 are 312, 624, 936. Because 312 is the smallest, it is the least common multiple.
The LCM of 24 and 52 is 312.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 8 and 39?
What is the LCM of 108 and 140?
What is the LCM of 120 and 36?
What is the LCM of 59 and 96?
What is the LCM of 62 and 69?