Solution: The LCM of 137 and 76 is 10412
Methods
How to find the LCM of 137 and 76 using Prime Factorization
One way to find the LCM of 137 and 76 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 137?
What are the Factors of 76?
Here is the prime factorization of 137:
13
7
1
137^1
13 7 1
And this is the prime factorization of 76:
2
2
×
1
9
1
2^2 × 19^1
2 2 × 1 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: 137, 2, 19
2
2
×
1
9
1
×
13
7
1
=
10412
2^2 × 19^1 × 137^1 = 10412
2 2 × 1 9 1 × 13 7 1 = 10412
Through this we see that the LCM of 137 and 76 is 10412.
How to Find the LCM of 137 and 76 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 137 and 76 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, 137 and 76:
What are the Multiples of 137?
What are the Multiples of 76?
Let’s take a look at the first 10 multiples for each of these numbers, 137 and 76:
First 10 Multiples of 137: 137, 274, 411, 548, 685, 822, 959, 1096, 1233, 1370
First 10 Multiples of 76: 76, 152, 228, 304, 380, 456, 532, 608, 684, 760
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 137 and 76 are 10412, 20824, 31236. Because 10412 is the smallest, it is the least common multiple.
The LCM of 137 and 76 is 10412.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 64 and 68?
What is the LCM of 34 and 136?
What is the LCM of 120 and 90?
What is the LCM of 50 and 39?
What is the LCM of 126 and 51?