Solution: The LCM of 34 and 20 is 340
Methods
How to find the LCM of 34 and 20 using Prime Factorization
One way to find the LCM of 34 and 20 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 20?
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 20:
2
2
×
5
1
2^2 × 5^1
2 2 × 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, 17, 5
2
2
×
5
1
×
1
7
1
=
340
2^2 × 5^1 × 17^1 = 340
2 2 × 5 1 × 1 7 1 = 340
Through this we see that the LCM of 34 and 20 is 340.
How to Find the LCM of 34 and 20 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 34 and 20 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 20:
What are the Multiples of 34?
What are the Multiples of 20?
Let’s take a look at the first 10 multiples for each of these numbers, 34 and 20:
First 10 Multiples of 34: 34, 68, 102, 136, 170, 204, 238, 272, 306, 340
First 10 Multiples of 20: 20, 40, 60, 80, 100, 120, 140, 160, 180, 200
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 20 are 340, 680, 1020. Because 340 is the smallest, it is the least common multiple.
The LCM of 34 and 20 is 340.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 111 and 130?
What is the LCM of 18 and 98?
What is the LCM of 29 and 135?
What is the LCM of 52 and 105?
What is the LCM of 86 and 150?