Solution: The LCM of 34 and 108 is 1836
Methods
How to find the LCM of 34 and 108 using Prime Factorization
One way to find the LCM of 34 and 108 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 34?
What are the Factors of 108?
Here is the prime factorization of 34:
2
1
×
1
7
1
2^1 × 17^1
2 1 × 1 7 1
And this is the prime factorization of 108:
2
2
×
3
3
2^2 × 3^3
2 2 × 3 3
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, 17, 3
2
2
×
3
3
×
1
7
1
=
1836
2^2 × 3^3 × 17^1 = 1836
2 2 × 3 3 × 1 7 1 = 1836
Through this we see that the LCM of 34 and 108 is 1836.
How to Find the LCM of 34 and 108 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 34 and 108 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, 34 and 108:
What are the Multiples of 34?
What are the Multiples of 108?
Let’s take a look at the first 10 multiples for each of these numbers, 34 and 108:
First 10 Multiples of 34: 34, 68, 102, 136, 170, 204, 238, 272, 306, 340
First 10 Multiples of 108: 108, 216, 324, 432, 540, 648, 756, 864, 972, 1080
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 34 and 108 are 1836, 3672, 5508. Because 1836 is the smallest, it is the least common multiple.
The LCM of 34 and 108 is 1836.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 85 and 48?
What is the LCM of 113 and 54?
What is the LCM of 4 and 11?
What is the LCM of 32 and 116?
What is the LCM of 42 and 150?