Solution: The LCM of 75 and 76 is 5700
Methods
How to find the LCM of 75 and 76 using Prime Factorization
One way to find the LCM of 75 and 76 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 76?
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 76:
2
2
×
1
9
1
2^2 × 19^1
2 2 × 1 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, 2, 19
2
2
×
3
1
×
5
2
×
1
9
1
=
5700
2^2 × 3^1 × 5^2 × 19^1 = 5700
2 2 × 3 1 × 5 2 × 1 9 1 = 5700
Through this we see that the LCM of 75 and 76 is 5700.
How to Find the LCM of 75 and 76 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 75 and 76 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 76:
What are the Multiples of 75?
What are the Multiples of 76?
Let’s take a look at the first 10 multiples for each of these numbers, 75 and 76:
First 10 Multiples of 75: 75, 150, 225, 300, 375, 450, 525, 600, 675, 750
First 10 Multiples of 76: 76, 152, 228, 304, 380, 456, 532, 608, 684, 760
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 76 are 5700, 11400, 17100. Because 5700 is the smallest, it is the least common multiple.
The LCM of 75 and 76 is 5700.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 62 and 139?
What is the LCM of 42 and 16?
What is the LCM of 29 and 90?
What is the LCM of 78 and 129?
What is the LCM of 59 and 144?