Solution: The LCM of 38 and 103 is 3914
Methods
How to find the LCM of 38 and 103 using Prime Factorization
One way to find the LCM of 38 and 103 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 38?
What are the Factors of 103?
Here is the prime factorization of 38:
2
1
×
1
9
1
2^1 × 19^1
2 1 × 1 9 1
And this is the prime factorization of 103:
10
3
1
103^1
10 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: 2, 19, 103
2
1
×
1
9
1
×
10
3
1
=
3914
2^1 × 19^1 × 103^1 = 3914
2 1 × 1 9 1 × 10 3 1 = 3914
Through this we see that the LCM of 38 and 103 is 3914.
How to Find the LCM of 38 and 103 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 38 and 103 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, 38 and 103:
What are the Multiples of 38?
What are the Multiples of 103?
Let’s take a look at the first 10 multiples for each of these numbers, 38 and 103:
First 10 Multiples of 38: 38, 76, 114, 152, 190, 228, 266, 304, 342, 380
First 10 Multiples of 103: 103, 206, 309, 412, 515, 618, 721, 824, 927, 1030
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 38 and 103 are 3914, 7828, 11742. Because 3914 is the smallest, it is the least common multiple.
The LCM of 38 and 103 is 3914.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 43 and 45?
What is the LCM of 63 and 8?
What is the LCM of 48 and 44?
What is the LCM of 122 and 54?
What is the LCM of 124 and 20?