Solution: The LCM of 52 and 50 is 1300
Methods
How to find the LCM of 52 and 50 using Prime Factorization
One way to find the LCM of 52 and 50 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 52?
What are the Factors of 50?
Here is the prime factorization of 52:
2
2
×
1
3
1
2^2 × 13^1
2 2 × 1 3 1
And this is the prime factorization of 50:
2
1
×
5
2
2^1 × 5^2
2 1 × 5 2
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, 13, 5
2
2
×
5
2
×
1
3
1
=
1300
2^2 × 5^2 × 13^1 = 1300
2 2 × 5 2 × 1 3 1 = 1300
Through this we see that the LCM of 52 and 50 is 1300.
How to Find the LCM of 52 and 50 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 52 and 50 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, 52 and 50:
What are the Multiples of 52?
What are the Multiples of 50?
Let’s take a look at the first 10 multiples for each of these numbers, 52 and 50:
First 10 Multiples of 52: 52, 104, 156, 208, 260, 312, 364, 416, 468, 520
First 10 Multiples of 50: 50, 100, 150, 200, 250, 300, 350, 400, 450, 500
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 52 and 50 are 1300, 2600, 3900. Because 1300 is the smallest, it is the least common multiple.
The LCM of 52 and 50 is 1300.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 28 and 143?
What is the LCM of 73 and 70?
What is the LCM of 20 and 11?
What is the LCM of 4 and 110?
What is the LCM of 17 and 85?