Solution: The LCM of 107 and 132 is 14124
Methods
How to find the LCM of 107 and 132 using Prime Factorization
One way to find the LCM of 107 and 132 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 107?
What are the Factors of 132?
Here is the prime factorization of 107:
10
7
1
107^1
10 7 1
And this is the prime factorization of 132:
2
2
×
3
1
×
1
1
1
2^2 × 3^1 × 11^1
2 2 × 3 1 × 1 1 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: 107, 2, 3, 11
2
2
×
3
1
×
1
1
1
×
10
7
1
=
14124
2^2 × 3^1 × 11^1 × 107^1 = 14124
2 2 × 3 1 × 1 1 1 × 10 7 1 = 14124
Through this we see that the LCM of 107 and 132 is 14124.
How to Find the LCM of 107 and 132 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 107 and 132 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, 107 and 132:
What are the Multiples of 107?
What are the Multiples of 132?
Let’s take a look at the first 10 multiples for each of these numbers, 107 and 132:
First 10 Multiples of 107: 107, 214, 321, 428, 535, 642, 749, 856, 963, 1070
First 10 Multiples of 132: 132, 264, 396, 528, 660, 792, 924, 1056, 1188, 1320
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 107 and 132 are 14124, 28248, 42372. Because 14124 is the smallest, it is the least common multiple.
The LCM of 107 and 132 is 14124.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 99 and 26?
What is the LCM of 102 and 9?
What is the LCM of 110 and 64?
What is the LCM of 124 and 14?
What is the LCM of 114 and 71?