Solution: The LCM of 51 and 95 is 4845
Methods
How to find the LCM of 51 and 95 using Prime Factorization
One way to find the LCM of 51 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 51?
What are the Factors of 95?
Here is the prime factorization of 51:
3
1
×
1
7
1
3^1 × 17^1
3 1 × 1 7 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: 3, 17, 5, 19
3
1
×
5
1
×
1
7
1
×
1
9
1
=
4845
3^1 × 5^1 × 17^1 × 19^1 = 4845
3 1 × 5 1 × 1 7 1 × 1 9 1 = 4845
Through this we see that the LCM of 51 and 95 is 4845.
How to Find the LCM of 51 and 95 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 51 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, 51 and 95:
What are the Multiples of 51?
What are the Multiples of 95?
Let’s take a look at the first 10 multiples for each of these numbers, 51 and 95:
First 10 Multiples of 51: 51, 102, 153, 204, 255, 306, 357, 408, 459, 510
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 51 and 95 are 4845, 9690, 14535. Because 4845 is the smallest, it is the least common multiple.
The LCM of 51 and 95 is 4845.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 16 and 94?
What is the LCM of 31 and 60?
What is the LCM of 82 and 42?
What is the LCM of 22 and 48?
What is the LCM of 108 and 124?