Solution: The LCM of 15 and 144 is 720
Methods
How to find the LCM of 15 and 144 using Prime Factorization
One way to find the LCM of 15 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 15?
What are the Factors of 144?
Here is the prime factorization of 15:
3
1
×
5
1
3^1 × 5^1
3 1 × 5 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: 3, 5, 2
2
4
×
3
2
×
5
1
=
720
2^4 × 3^2 × 5^1 = 720
2 4 × 3 2 × 5 1 = 720
Through this we see that the LCM of 15 and 144 is 720.
How to Find the LCM of 15 and 144 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 15 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, 15 and 144:
What are the Multiples of 15?
What are the Multiples of 144?
Let’s take a look at the first 10 multiples for each of these numbers, 15 and 144:
First 10 Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, 135, 150
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 15 and 144 are 720, 1440, 2160. Because 720 is the smallest, it is the least common multiple.
The LCM of 15 and 144 is 720.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 117 and 5?
What is the LCM of 141 and 34?
What is the LCM of 115 and 85?
What is the LCM of 136 and 56?
What is the LCM of 111 and 63?