Solution: The LCM of 84 and 134 is 5628
Methods
How to find the LCM of 84 and 134 using Prime Factorization
One way to find the LCM of 84 and 134 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 84?
What are the Factors of 134?
Here is the prime factorization of 84:
2
2
×
3
1
×
7
1
2^2 × 3^1 × 7^1
2 2 × 3 1 × 7 1
And this is the prime factorization of 134:
2
1
×
6
7
1
2^1 × 67^1
2 1 × 6 7 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, 7, 67
2
2
×
3
1
×
7
1
×
6
7
1
=
5628
2^2 × 3^1 × 7^1 × 67^1 = 5628
2 2 × 3 1 × 7 1 × 6 7 1 = 5628
Through this we see that the LCM of 84 and 134 is 5628.
How to Find the LCM of 84 and 134 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 84 and 134 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, 84 and 134:
What are the Multiples of 84?
What are the Multiples of 134?
Let’s take a look at the first 10 multiples for each of these numbers, 84 and 134:
First 10 Multiples of 84: 84, 168, 252, 336, 420, 504, 588, 672, 756, 840
First 10 Multiples of 134: 134, 268, 402, 536, 670, 804, 938, 1072, 1206, 1340
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 84 and 134 are 5628, 11256, 16884. Because 5628 is the smallest, it is the least common multiple.
The LCM of 84 and 134 is 5628.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 73 and 103?
What is the LCM of 35 and 137?
What is the LCM of 41 and 54?
What is the LCM of 70 and 118?
What is the LCM of 67 and 59?