Solution: The LCM of 89 and 40 is 3560
Methods
How to find the LCM of 89 and 40 using Prime Factorization
One way to find the LCM of 89 and 40 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 89?
What are the Factors of 40?
Here is the prime factorization of 89:
8
9
1
89^1
8 9 1
And this is the prime factorization of 40:
2
3
×
5
1
2^3 × 5^1
2 3 × 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: 89, 2, 5
2
3
×
5
1
×
8
9
1
=
3560
2^3 × 5^1 × 89^1 = 3560
2 3 × 5 1 × 8 9 1 = 3560
Through this we see that the LCM of 89 and 40 is 3560.
How to Find the LCM of 89 and 40 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 89 and 40 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, 89 and 40:
What are the Multiples of 89?
What are the Multiples of 40?
Let’s take a look at the first 10 multiples for each of these numbers, 89 and 40:
First 10 Multiples of 89: 89, 178, 267, 356, 445, 534, 623, 712, 801, 890
First 10 Multiples of 40: 40, 80, 120, 160, 200, 240, 280, 320, 360, 400
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 89 and 40 are 3560, 7120, 10680. Because 3560 is the smallest, it is the least common multiple.
The LCM of 89 and 40 is 3560.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 121 and 49?
What is the LCM of 18 and 128?
What is the LCM of 117 and 137?
What is the LCM of 107 and 9?
What is the LCM of 29 and 148?