Solution: The LCM of 60 and 95 is 1140
Methods
How to find the LCM of 60 and 95 using Prime Factorization
One way to find the LCM of 60 and 95 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 60?
What are the Factors of 95?
Here is the prime factorization of 60:
2
2
×
3
1
×
5
1
2^2 × 3^1 × 5^1
2 2 × 3 1 × 5 1
And this is the prime factorization of 95:
5
1
×
1
9
1
5^1 × 19^1
5 1 × 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: 2, 3, 5, 19
2
2
×
3
1
×
5
1
×
1
9
1
=
1140
2^2 × 3^1 × 5^1 × 19^1 = 1140
2 2 × 3 1 × 5 1 × 1 9 1 = 1140
Through this we see that the LCM of 60 and 95 is 1140.
How to Find the LCM of 60 and 95 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 60 and 95 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, 60 and 95:
What are the Multiples of 60?
What are the Multiples of 95?
Let’s take a look at the first 10 multiples for each of these numbers, 60 and 95:
First 10 Multiples of 60: 60, 120, 180, 240, 300, 360, 420, 480, 540, 600
First 10 Multiples of 95: 95, 190, 285, 380, 475, 570, 665, 760, 855, 950
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 60 and 95 are 1140, 2280, 3420. Because 1140 is the smallest, it is the least common multiple.
The LCM of 60 and 95 is 1140.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 4 and 66?
What is the LCM of 146 and 129?
What is the LCM of 116 and 38?
What is the LCM of 76 and 78?
What is the LCM of 80 and 99?