Solution: The LCM of 121 and 89 is 10769
Methods
How to find the LCM of 121 and 89 using Prime Factorization
One way to find the LCM of 121 and 89 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 89?
Here is the prime factorization of 121:
1
1
2
11^2
1 1 2
And this is the prime factorization of 89:
8
9
1
89^1
8 9 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, 89
1
1
2
×
8
9
1
=
10769
11^2 × 89^1 = 10769
1 1 2 × 8 9 1 = 10769
Through this we see that the LCM of 121 and 89 is 10769.
How to Find the LCM of 121 and 89 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 121 and 89 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 89:
What are the Multiples of 121?
What are the Multiples of 89?
Let’s take a look at the first 10 multiples for each of these numbers, 121 and 89:
First 10 Multiples of 121: 121, 242, 363, 484, 605, 726, 847, 968, 1089, 1210
First 10 Multiples of 89: 89, 178, 267, 356, 445, 534, 623, 712, 801, 890
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 89 are 10769, 21538, 32307. Because 10769 is the smallest, it is the least common multiple.
The LCM of 121 and 89 is 10769.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 32 and 125?
What is the LCM of 127 and 45?
What is the LCM of 65 and 16?
What is the LCM of 18 and 92?
What is the LCM of 99 and 104?