Solution: The LCM of 38 and 106 is 2014
Methods
How to find the LCM of 38 and 106 using Prime Factorization
One way to find the LCM of 38 and 106 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 106?
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 106:
2
1
×
5
3
1
2^1 × 53^1
2 1 × 5 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, 53
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 38 and 106 is 2014.
How to Find the LCM of 38 and 106 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 38 and 106 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 106:
What are the Multiples of 38?
What are the Multiples of 106?
Let’s take a look at the first 10 multiples for each of these numbers, 38 and 106:
First 10 Multiples of 38: 38, 76, 114, 152, 190, 228, 266, 304, 342, 380
First 10 Multiples of 106: 106, 212, 318, 424, 530, 636, 742, 848, 954, 1060
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 106 are 2014, 4028, 6042. Because 2014 is the smallest, it is the least common multiple.
The LCM of 38 and 106 is 2014.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 100 and 65?
What is the LCM of 20 and 76?
What is the LCM of 126 and 131?
What is the LCM of 46 and 87?
What is the LCM of 34 and 16?