Solution: The LCM of 53 and 38 is 2014
Methods
How to find the LCM of 53 and 38 using Prime Factorization
One way to find the LCM of 53 and 38 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 53?
What are the Factors of 38?
Here is the prime factorization of 53:
5
3
1
53^1
5 3 1
And this is the prime factorization of 38:
2
1
×
1
9
1
2^1 × 19^1
2 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: 53, 2, 19
2
1
×
1
9
1
×
5
3
1
=
2014
2^1 × 19^1 × 53^1 = 2014
2 1 × 1 9 1 × 5 3 1 = 2014
Through this we see that the LCM of 53 and 38 is 2014.
How to Find the LCM of 53 and 38 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 53 and 38 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, 53 and 38:
What are the Multiples of 53?
What are the Multiples of 38?
Let’s take a look at the first 10 multiples for each of these numbers, 53 and 38:
First 10 Multiples of 53: 53, 106, 159, 212, 265, 318, 371, 424, 477, 530
First 10 Multiples of 38: 38, 76, 114, 152, 190, 228, 266, 304, 342, 380
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 53 and 38 are 2014, 4028, 6042. Because 2014 is the smallest, it is the least common multiple.
The LCM of 53 and 38 is 2014.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 120 and 135?
What is the LCM of 139 and 143?
What is the LCM of 12 and 74?
What is the LCM of 37 and 142?
What is the LCM of 39 and 19?