Solution: The LCM of 7 and 52 is 364
Methods
How to find the LCM of 7 and 52 using Prime Factorization
One way to find the LCM of 7 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 7?
What are the Factors of 52?
Here is the prime factorization of 7:
7
1
7^1
7 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: 7, 2, 13
2
2
×
7
1
×
1
3
1
=
364
2^2 × 7^1 × 13^1 = 364
2 2 × 7 1 × 1 3 1 = 364
Through this we see that the LCM of 7 and 52 is 364.
How to Find the LCM of 7 and 52 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 7 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, 7 and 52:
What are the Multiples of 7?
What are the Multiples of 52?
Let’s take a look at the first 10 multiples for each of these numbers, 7 and 52:
First 10 Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70
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 7 and 52 are 364, 728, 1092. Because 364 is the smallest, it is the least common multiple.
The LCM of 7 and 52 is 364.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 80 and 88?
What is the LCM of 41 and 30?
What is the LCM of 87 and 125?
What is the LCM of 89 and 49?
What is the LCM of 106 and 60?