Solution: The LCM of 90 and 75 is 450
Methods
How to find the LCM of 90 and 75 using Prime Factorization
One way to find the LCM of 90 and 75 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 90?
What are the Factors of 75?
Here is the prime factorization of 90:
2
1
×
3
2
×
5
1
2^1 × 3^2 × 5^1
2 1 × 3 2 × 5 1
And this is the prime factorization of 75:
3
1
×
5
2
3^1 × 5^2
3 1 × 5 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, 5
2
1
×
3
2
×
5
2
=
450
2^1 × 3^2 × 5^2 = 450
2 1 × 3 2 × 5 2 = 450
Through this we see that the LCM of 90 and 75 is 450.
How to Find the LCM of 90 and 75 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 90 and 75 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, 90 and 75:
What are the Multiples of 90?
What are the Multiples of 75?
Let’s take a look at the first 10 multiples for each of these numbers, 90 and 75:
First 10 Multiples of 90: 90, 180, 270, 360, 450, 540, 630, 720, 810, 900
First 10 Multiples of 75: 75, 150, 225, 300, 375, 450, 525, 600, 675, 750
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 90 and 75 are 450, 900, 1350. Because 450 is the smallest, it is the least common multiple.
The LCM of 90 and 75 is 450.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 119 and 10?
What is the LCM of 113 and 124?
What is the LCM of 66 and 127?
What is the LCM of 30 and 130?
What is the LCM of 40 and 57?