Solution: The LCM of 75 and 116 is 8700
Methods
How to find the LCM of 75 and 116 using Prime Factorization
One way to find the LCM of 75 and 116 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 75?
What are the Factors of 116?
Here is the prime factorization of 75:
3
1
×
5
2
3^1 × 5^2
3 1 × 5 2
And this is the prime factorization of 116:
2
2
×
2
9
1
2^2 × 29^1
2 2 × 2 9 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: 3, 5, 2, 29
2
2
×
3
1
×
5
2
×
2
9
1
=
8700
2^2 × 3^1 × 5^2 × 29^1 = 8700
2 2 × 3 1 × 5 2 × 2 9 1 = 8700
Through this we see that the LCM of 75 and 116 is 8700.
How to Find the LCM of 75 and 116 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 75 and 116 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, 75 and 116:
What are the Multiples of 75?
What are the Multiples of 116?
Let’s take a look at the first 10 multiples for each of these numbers, 75 and 116:
First 10 Multiples of 75: 75, 150, 225, 300, 375, 450, 525, 600, 675, 750
First 10 Multiples of 116: 116, 232, 348, 464, 580, 696, 812, 928, 1044, 1160
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 75 and 116 are 8700, 17400, 26100. Because 8700 is the smallest, it is the least common multiple.
The LCM of 75 and 116 is 8700.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 41 and 131?
What is the LCM of 10 and 101?
What is the LCM of 114 and 2?
What is the LCM of 74 and 9?
What is the LCM of 137 and 96?