Solution: The LCM of 144 and 85 is 12240
Methods
How to find the LCM of 144 and 85 using Prime Factorization
One way to find the LCM of 144 and 85 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 144?
What are the Factors of 85?
Here is the prime factorization of 144:
2
4
×
3
2
2^4 × 3^2
2 4 × 3 2
And this is the prime factorization of 85:
5
1
×
1
7
1
5^1 × 17^1
5 1 × 1 7 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, 5, 17
2
4
×
3
2
×
5
1
×
1
7
1
=
12240
2^4 × 3^2 × 5^1 × 17^1 = 12240
2 4 × 3 2 × 5 1 × 1 7 1 = 12240
Through this we see that the LCM of 144 and 85 is 12240.
How to Find the LCM of 144 and 85 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 144 and 85 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, 144 and 85:
What are the Multiples of 144?
What are the Multiples of 85?
Let’s take a look at the first 10 multiples for each of these numbers, 144 and 85:
First 10 Multiples of 144: 144, 288, 432, 576, 720, 864, 1008, 1152, 1296, 1440
First 10 Multiples of 85: 85, 170, 255, 340, 425, 510, 595, 680, 765, 850
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 144 and 85 are 12240, 24480, 36720. Because 12240 is the smallest, it is the least common multiple.
The LCM of 144 and 85 is 12240.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 35 and 11?
What is the LCM of 38 and 99?
What is the LCM of 78 and 149?
What is the LCM of 119 and 54?
What is the LCM of 97 and 95?