Solution: The LCM of 114 and 144 is 2736
Methods
How to find the LCM of 114 and 144 using Prime Factorization
One way to find the LCM of 114 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 114?
What are the Factors of 144?
Here is the prime factorization of 114:
2
1
×
3
1
×
1
9
1
2^1 × 3^1 × 19^1
2 1 × 3 1 × 1 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: 2, 3, 19
2
4
×
3
2
×
1
9
1
=
2736
2^4 × 3^2 × 19^1 = 2736
2 4 × 3 2 × 1 9 1 = 2736
Through this we see that the LCM of 114 and 144 is 2736.
How to Find the LCM of 114 and 144 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 114 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, 114 and 144:
What are the Multiples of 114?
What are the Multiples of 144?
Let’s take a look at the first 10 multiples for each of these numbers, 114 and 144:
First 10 Multiples of 114: 114, 228, 342, 456, 570, 684, 798, 912, 1026, 1140
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 114 and 144 are 2736, 5472, 8208. Because 2736 is the smallest, it is the least common multiple.
The LCM of 114 and 144 is 2736.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 10 and 72?
What is the LCM of 17 and 1?
What is the LCM of 129 and 16?
What is the LCM of 63 and 24?
What is the LCM of 119 and 110?