Solution: The LCM of 109 and 75 is 8175
Methods
How to find the LCM of 109 and 75 using Prime Factorization
One way to find the LCM of 109 and 75 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 109?
What are the Factors of 75?
Here is the prime factorization of 109:
10
9
1
109^1
10 9 1
And this is the prime factorization of 75:
3
1
×
5
2
3^1 × 5^2
3 1 × 5 2
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: 109, 3, 5
3
1
×
5
2
×
10
9
1
=
8175
3^1 × 5^2 × 109^1 = 8175
3 1 × 5 2 × 10 9 1 = 8175
Through this we see that the LCM of 109 and 75 is 8175.
How to Find the LCM of 109 and 75 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 109 and 75 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, 109 and 75:
What are the Multiples of 109?
What are the Multiples of 75?
Let’s take a look at the first 10 multiples for each of these numbers, 109 and 75:
First 10 Multiples of 109: 109, 218, 327, 436, 545, 654, 763, 872, 981, 1090
First 10 Multiples of 75: 75, 150, 225, 300, 375, 450, 525, 600, 675, 750
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 109 and 75 are 8175, 16350, 24525. Because 8175 is the smallest, it is the least common multiple.
The LCM of 109 and 75 is 8175.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 108 and 18?
What is the LCM of 39 and 96?
What is the LCM of 15 and 106?
What is the LCM of 47 and 23?
What is the LCM of 131 and 126?