Solution: The LCM of 118 and 18 is 1062
Methods
How to find the LCM of 118 and 18 using Prime Factorization
One way to find the LCM of 118 and 18 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 118?
What are the Factors of 18?
Here is the prime factorization of 118:
2
1
×
5
9
1
2^1 × 59^1
2 1 × 5 9 1
And this is the prime factorization of 18:
2
1
×
3
2
2^1 × 3^2
2 1 × 3 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, 59, 3
2
1
×
3
2
×
5
9
1
=
1062
2^1 × 3^2 × 59^1 = 1062
2 1 × 3 2 × 5 9 1 = 1062
Through this we see that the LCM of 118 and 18 is 1062.
How to Find the LCM of 118 and 18 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 118 and 18 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, 118 and 18:
What are the Multiples of 118?
What are the Multiples of 18?
Let’s take a look at the first 10 multiples for each of these numbers, 118 and 18:
First 10 Multiples of 118: 118, 236, 354, 472, 590, 708, 826, 944, 1062, 1180
First 10 Multiples of 18: 18, 36, 54, 72, 90, 108, 126, 144, 162, 180
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 118 and 18 are 1062, 2124, 3186. Because 1062 is the smallest, it is the least common multiple.
The LCM of 118 and 18 is 1062.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 115 and 61?
What is the LCM of 60 and 28?
What is the LCM of 55 and 83?
What is the LCM of 42 and 35?
What is the LCM of 126 and 88?