Solution: The LCM of 75 and 74 is 5550
Methods
How to find the LCM of 75 and 74 using Prime Factorization
One way to find the LCM of 75 and 74 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 74?
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 74:
2
1
×
3
7
1
2^1 × 37^1
2 1 × 3 7 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, 37
2
1
×
3
1
×
5
2
×
3
7
1
=
5550
2^1 × 3^1 × 5^2 × 37^1 = 5550
2 1 × 3 1 × 5 2 × 3 7 1 = 5550
Through this we see that the LCM of 75 and 74 is 5550.
How to Find the LCM of 75 and 74 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 75 and 74 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 74:
What are the Multiples of 75?
What are the Multiples of 74?
Let’s take a look at the first 10 multiples for each of these numbers, 75 and 74:
First 10 Multiples of 75: 75, 150, 225, 300, 375, 450, 525, 600, 675, 750
First 10 Multiples of 74: 74, 148, 222, 296, 370, 444, 518, 592, 666, 740
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 74 are 5550, 11100, 16650. Because 5550 is the smallest, it is the least common multiple.
The LCM of 75 and 74 is 5550.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 57 and 18?
What is the LCM of 78 and 56?
What is the LCM of 38 and 126?
What is the LCM of 120 and 99?
What is the LCM of 146 and 32?