Solution: The LCM of 121 and 90 is 10890
Methods
How to find the LCM of 121 and 90 using Prime Factorization
One way to find the LCM of 121 and 90 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 121?
What are the Factors of 90?
Here is the prime factorization of 121:
1
1
2
11^2
1 1 2
And this is the prime factorization of 90:
2
1
×
3
2
×
5
1
2^1 × 3^2 × 5^1
2 1 × 3 2 × 5 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: 11, 2, 3, 5
2
1
×
3
2
×
5
1
×
1
1
2
=
10890
2^1 × 3^2 × 5^1 × 11^2 = 10890
2 1 × 3 2 × 5 1 × 1 1 2 = 10890
Through this we see that the LCM of 121 and 90 is 10890.
How to Find the LCM of 121 and 90 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 121 and 90 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, 121 and 90:
What are the Multiples of 121?
What are the Multiples of 90?
Let’s take a look at the first 10 multiples for each of these numbers, 121 and 90:
First 10 Multiples of 121: 121, 242, 363, 484, 605, 726, 847, 968, 1089, 1210
First 10 Multiples of 90: 90, 180, 270, 360, 450, 540, 630, 720, 810, 900
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 121 and 90 are 10890, 21780, 32670. Because 10890 is the smallest, it is the least common multiple.
The LCM of 121 and 90 is 10890.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 93 and 49?
What is the LCM of 126 and 119?
What is the LCM of 41 and 98?
What is the LCM of 145 and 117?
What is the LCM of 70 and 20?