Solution: The LCM of 52 and 122 is 3172
Methods
How to find the LCM of 52 and 122 using Prime Factorization
One way to find the LCM of 52 and 122 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 122?
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 122:
2
1
×
6
1
1
2^1 × 61^1
2 1 × 6 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, 61
2
2
×
1
3
1
×
6
1
1
=
3172
2^2 × 13^1 × 61^1 = 3172
2 2 × 1 3 1 × 6 1 1 = 3172
Through this we see that the LCM of 52 and 122 is 3172.
How to Find the LCM of 52 and 122 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 52 and 122 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 122:
What are the Multiples of 52?
What are the Multiples of 122?
Let’s take a look at the first 10 multiples for each of these numbers, 52 and 122:
First 10 Multiples of 52: 52, 104, 156, 208, 260, 312, 364, 416, 468, 520
First 10 Multiples of 122: 122, 244, 366, 488, 610, 732, 854, 976, 1098, 1220
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 122 are 3172, 6344, 9516. Because 3172 is the smallest, it is the least common multiple.
The LCM of 52 and 122 is 3172.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 50 and 126?
What is the LCM of 132 and 142?
What is the LCM of 68 and 83?
What is the LCM of 118 and 112?
What is the LCM of 49 and 20?