Solution: The LCM of 90 and 112 is 5040
Methods
How to find the LCM of 90 and 112 using Prime Factorization
One way to find the LCM of 90 and 112 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 112?
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 112:
2
4
×
7
1
2^4 × 7^1
2 4 × 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, 7
2
4
×
3
2
×
5
1
×
7
1
=
5040
2^4 × 3^2 × 5^1 × 7^1 = 5040
2 4 × 3 2 × 5 1 × 7 1 = 5040
Through this we see that the LCM of 90 and 112 is 5040.
How to Find the LCM of 90 and 112 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 90 and 112 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 112:
What are the Multiples of 90?
What are the Multiples of 112?
Let’s take a look at the first 10 multiples for each of these numbers, 90 and 112:
First 10 Multiples of 90: 90, 180, 270, 360, 450, 540, 630, 720, 810, 900
First 10 Multiples of 112: 112, 224, 336, 448, 560, 672, 784, 896, 1008, 1120
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 112 are 5040, 10080, 15120. Because 5040 is the smallest, it is the least common multiple.
The LCM of 90 and 112 is 5040.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 131 and 74?
What is the LCM of 100 and 18?
What is the LCM of 37 and 77?
What is the LCM of 107 and 20?
What is the LCM of 121 and 117?