Solution: The LCM of 18 and 30 is 90
Methods
How to find the LCM of 18 and 30 using Prime Factorization
One way to find the LCM of 18 and 30 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 18?
What are the Factors of 30?
Here is the prime factorization of 18:
2
1
×
3
2
2^1 × 3^2
2 1 × 3 2
And this is the prime factorization of 30:
2
1
×
3
1
×
5
1
2^1 × 3^1 × 5^1
2 1 × 3 1 × 5 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, 3, 5
2
1
×
3
2
×
5
1
=
90
2^1 × 3^2 × 5^1 = 90
2 1 × 3 2 × 5 1 = 90
Through this we see that the LCM of 18 and 30 is 90.
How to Find the LCM of 18 and 30 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 18 and 30 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, 18 and 30:
What are the Multiples of 18?
What are the Multiples of 30?
Let’s take a look at the first 10 multiples for each of these numbers, 18 and 30:
First 10 Multiples of 18: 18, 36, 54, 72, 90, 108, 126, 144, 162, 180
First 10 Multiples of 30: 30, 60, 90, 120, 150, 180, 210, 240, 270, 300
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 18 and 30 are 90, 180, 270. Because 90 is the smallest, it is the least common multiple.
The LCM of 18 and 30 is 90.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 55 and 35?
What is the LCM of 6 and 14?
What is the LCM of 67 and 120?
What is the LCM of 88 and 1?
What is the LCM of 112 and 75?