Solution: The LCM of 76 and 37 is 2812
Methods
How to find the LCM of 76 and 37 using Prime Factorization
One way to find the LCM of 76 and 37 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 76?
What are the Factors of 37?
Here is the prime factorization of 76:
2
2
×
1
9
1
2^2 × 19^1
2 2 × 1 9 1
And this is the prime factorization of 37:
3
7
1
37^1
3 7 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, 19, 37
2
2
×
1
9
1
×
3
7
1
=
2812
2^2 × 19^1 × 37^1 = 2812
2 2 × 1 9 1 × 3 7 1 = 2812
Through this we see that the LCM of 76 and 37 is 2812.
How to Find the LCM of 76 and 37 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 76 and 37 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, 76 and 37:
What are the Multiples of 76?
What are the Multiples of 37?
Let’s take a look at the first 10 multiples for each of these numbers, 76 and 37:
First 10 Multiples of 76: 76, 152, 228, 304, 380, 456, 532, 608, 684, 760
First 10 Multiples of 37: 37, 74, 111, 148, 185, 222, 259, 296, 333, 370
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 76 and 37 are 2812, 5624, 8436. Because 2812 is the smallest, it is the least common multiple.
The LCM of 76 and 37 is 2812.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 90 and 28?
What is the LCM of 124 and 112?
What is the LCM of 82 and 48?
What is the LCM of 142 and 130?
What is the LCM of 6 and 127?