Solution: The LCM of 132 and 101 is 13332
Methods
How to find the LCM of 132 and 101 using Prime Factorization
One way to find the LCM of 132 and 101 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 132?
What are the Factors of 101?
Here 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
And this is the prime factorization of 101:
10
1
1
101^1
10 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: 2, 3, 11, 101
2
2
×
3
1
×
1
1
1
×
10
1
1
=
13332
2^2 × 3^1 × 11^1 × 101^1 = 13332
2 2 × 3 1 × 1 1 1 × 10 1 1 = 13332
Through this we see that the LCM of 132 and 101 is 13332.
How to Find the LCM of 132 and 101 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 132 and 101 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, 132 and 101:
What are the Multiples of 132?
What are the Multiples of 101?
Let’s take a look at the first 10 multiples for each of these numbers, 132 and 101:
First 10 Multiples of 132: 132, 264, 396, 528, 660, 792, 924, 1056, 1188, 1320
First 10 Multiples of 101: 101, 202, 303, 404, 505, 606, 707, 808, 909, 1010
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 132 and 101 are 13332, 26664, 39996. Because 13332 is the smallest, it is the least common multiple.
The LCM of 132 and 101 is 13332.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 89 and 118?
What is the LCM of 15 and 71?
What is the LCM of 28 and 62?
What is the LCM of 103 and 40?
What is the LCM of 29 and 67?