Solution: The LCM of 59 and 144 is 8496
Methods
How to find the LCM of 59 and 144 using Prime Factorization
One way to find the LCM of 59 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 59?
What are the Factors of 144?
Here is the prime factorization of 59:
5
9
1
59^1
5 9 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: 59, 2, 3
2
4
×
3
2
×
5
9
1
=
8496
2^4 × 3^2 × 59^1 = 8496
2 4 × 3 2 × 5 9 1 = 8496
Through this we see that the LCM of 59 and 144 is 8496.
How to Find the LCM of 59 and 144 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 59 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, 59 and 144:
What are the Multiples of 59?
What are the Multiples of 144?
Let’s take a look at the first 10 multiples for each of these numbers, 59 and 144:
First 10 Multiples of 59: 59, 118, 177, 236, 295, 354, 413, 472, 531, 590
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 59 and 144 are 8496, 16992, 25488. Because 8496 is the smallest, it is the least common multiple.
The LCM of 59 and 144 is 8496.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 127 and 28?
What is the LCM of 144 and 29?
What is the LCM of 119 and 96?
What is the LCM of 140 and 126?
What is the LCM of 146 and 105?