Solution: The LCM of 111 and 38 is 4218
Methods
How to find the LCM of 111 and 38 using Prime Factorization
One way to find the LCM of 111 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 111?
What are the Factors of 38?
Here is the prime factorization of 111:
3
1
×
3
7
1
3^1 × 37^1
3 1 × 3 7 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: 3, 37, 2, 19
2
1
×
3
1
×
1
9
1
×
3
7
1
=
4218
2^1 × 3^1 × 19^1 × 37^1 = 4218
2 1 × 3 1 × 1 9 1 × 3 7 1 = 4218
Through this we see that the LCM of 111 and 38 is 4218.
How to Find the LCM of 111 and 38 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 111 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, 111 and 38:
What are the Multiples of 111?
What are the Multiples of 38?
Let’s take a look at the first 10 multiples for each of these numbers, 111 and 38:
First 10 Multiples of 111: 111, 222, 333, 444, 555, 666, 777, 888, 999, 1110
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 111 and 38 are 4218, 8436, 12654. Because 4218 is the smallest, it is the least common multiple.
The LCM of 111 and 38 is 4218.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 19 and 131?
What is the LCM of 85 and 82?
What is the LCM of 101 and 116?
What is the LCM of 54 and 46?
What is the LCM of 29 and 93?