Solution: The LCM of 75 and 11 is 825
Methods
How to find the LCM of 75 and 11 using Prime Factorization
One way to find the LCM of 75 and 11 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 11?
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 11:
1
1
1
11^1
1 1 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, 11
3
1
×
5
2
×
1
1
1
=
825
3^1 × 5^2 × 11^1 = 825
3 1 × 5 2 × 1 1 1 = 825
Through this we see that the LCM of 75 and 11 is 825.
How to Find the LCM of 75 and 11 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 75 and 11 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 11:
What are the Multiples of 75?
What are the Multiples of 11?
Let’s take a look at the first 10 multiples for each of these numbers, 75 and 11:
First 10 Multiples of 75: 75, 150, 225, 300, 375, 450, 525, 600, 675, 750
First 10 Multiples of 11: 11, 22, 33, 44, 55, 66, 77, 88, 99, 110
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 11 are 825, 1650, 2475. Because 825 is the smallest, it is the least common multiple.
The LCM of 75 and 11 is 825.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 85 and 117?
What is the LCM of 113 and 53?
What is the LCM of 100 and 93?
What is the LCM of 97 and 80?
What is the LCM of 144 and 114?