Solution: The LCM of 75 and 89 is 6675
Methods
How to find the LCM of 75 and 89 using Prime Factorization
One way to find the LCM of 75 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 75?
What are the Factors of 89?
Here is the prime factorization of 75:
3
1
×
5
2
3^1 × 5^2
3 1 × 5 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: 3, 5, 89
3
1
×
5
2
×
8
9
1
=
6675
3^1 × 5^2 × 89^1 = 6675
3 1 × 5 2 × 8 9 1 = 6675
Through this we see that the LCM of 75 and 89 is 6675.
How to Find the LCM of 75 and 89 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 75 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, 75 and 89:
What are the Multiples of 75?
What are the Multiples of 89?
Let’s take a look at the first 10 multiples for each of these numbers, 75 and 89:
First 10 Multiples of 75: 75, 150, 225, 300, 375, 450, 525, 600, 675, 750
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 75 and 89 are 6675, 13350, 20025. Because 6675 is the smallest, it is the least common multiple.
The LCM of 75 and 89 is 6675.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 98 and 33?
What is the LCM of 16 and 96?
What is the LCM of 13 and 63?
What is the LCM of 41 and 60?
What is the LCM of 73 and 89?