Solution: The LCM of 75 and 130 is 1950
Methods
How to find the LCM of 75 and 130 using Prime Factorization
One way to find the LCM of 75 and 130 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 130?
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 130:
2
1
×
5
1
×
1
3
1
2^1 × 5^1 × 13^1
2 1 × 5 1 × 1 3 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, 13
2
1
×
3
1
×
5
2
×
1
3
1
=
1950
2^1 × 3^1 × 5^2 × 13^1 = 1950
2 1 × 3 1 × 5 2 × 1 3 1 = 1950
Through this we see that the LCM of 75 and 130 is 1950.
How to Find the LCM of 75 and 130 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 75 and 130 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 130:
What are the Multiples of 75?
What are the Multiples of 130?
Let’s take a look at the first 10 multiples for each of these numbers, 75 and 130:
First 10 Multiples of 75: 75, 150, 225, 300, 375, 450, 525, 600, 675, 750
First 10 Multiples of 130: 130, 260, 390, 520, 650, 780, 910, 1040, 1170, 1300
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 130 are 1950, 3900, 5850. Because 1950 is the smallest, it is the least common multiple.
The LCM of 75 and 130 is 1950.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 31 and 128?
What is the LCM of 134 and 21?
What is the LCM of 129 and 52?
What is the LCM of 132 and 42?
What is the LCM of 77 and 149?