Solution: The LCM of 91 and 144 is 13104
Methods
How to find the LCM of 91 and 144 using Prime Factorization
One way to find the LCM of 91 and 144 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 91?
What are the Factors of 144?
Here is the prime factorization of 91:
7
1
×
1
3
1
7^1 × 13^1
7 1 × 1 3 1
And this is the prime factorization of 144:
2
4
×
3
2
2^4 × 3^2
2 4 × 3 2
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: 7, 13, 2, 3
2
4
×
3
2
×
7
1
×
1
3
1
=
13104
2^4 × 3^2 × 7^1 × 13^1 = 13104
2 4 × 3 2 × 7 1 × 1 3 1 = 13104
Through this we see that the LCM of 91 and 144 is 13104.
How to Find the LCM of 91 and 144 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 91 and 144 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, 91 and 144:
What are the Multiples of 91?
What are the Multiples of 144?
Let’s take a look at the first 10 multiples for each of these numbers, 91 and 144:
First 10 Multiples of 91: 91, 182, 273, 364, 455, 546, 637, 728, 819, 910
First 10 Multiples of 144: 144, 288, 432, 576, 720, 864, 1008, 1152, 1296, 1440
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 91 and 144 are 13104, 26208, 39312. Because 13104 is the smallest, it is the least common multiple.
The LCM of 91 and 144 is 13104.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 118 and 135?
What is the LCM of 80 and 74?
What is the LCM of 93 and 104?
What is the LCM of 7 and 147?
What is the LCM of 10 and 8?