Solution: The LCM of 18 and 62 is 558
Methods
How to find the LCM of 18 and 62 using Prime Factorization
One way to find the LCM of 18 and 62 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 62?
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 62:
2
1
×
3
1
1
2^1 × 31^1
2 1 × 3 1 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, 31
2
1
×
3
2
×
3
1
1
=
558
2^1 × 3^2 × 31^1 = 558
2 1 × 3 2 × 3 1 1 = 558
Through this we see that the LCM of 18 and 62 is 558.
How to Find the LCM of 18 and 62 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 18 and 62 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 62:
What are the Multiples of 18?
What are the Multiples of 62?
Let’s take a look at the first 10 multiples for each of these numbers, 18 and 62:
First 10 Multiples of 18: 18, 36, 54, 72, 90, 108, 126, 144, 162, 180
First 10 Multiples of 62: 62, 124, 186, 248, 310, 372, 434, 496, 558, 620
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 62 are 558, 1116, 1674. Because 558 is the smallest, it is the least common multiple.
The LCM of 18 and 62 is 558.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 19 and 141?
What is the LCM of 73 and 22?
What is the LCM of 9 and 36?
What is the LCM of 28 and 131?
What is the LCM of 129 and 105?