Solution: The LCM of 115 and 52 is 5980
Methods
How to find the LCM of 115 and 52 using Prime Factorization
One way to find the LCM of 115 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 115?
What are the Factors of 52?
Here is the prime factorization of 115:
5
1
×
2
3
1
5^1 × 23^1
5 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: 5, 23, 2, 13
2
2
×
5
1
×
1
3
1
×
2
3
1
=
5980
2^2 × 5^1 × 13^1 × 23^1 = 5980
2 2 × 5 1 × 1 3 1 × 2 3 1 = 5980
Through this we see that the LCM of 115 and 52 is 5980.
How to Find the LCM of 115 and 52 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 115 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, 115 and 52:
What are the Multiples of 115?
What are the Multiples of 52?
Let’s take a look at the first 10 multiples for each of these numbers, 115 and 52:
First 10 Multiples of 115: 115, 230, 345, 460, 575, 690, 805, 920, 1035, 1150
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 115 and 52 are 5980, 11960, 17940. Because 5980 is the smallest, it is the least common multiple.
The LCM of 115 and 52 is 5980.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 55 and 3?
What is the LCM of 114 and 39?
What is the LCM of 117 and 50?
What is the LCM of 119 and 69?
What is the LCM of 53 and 141?