Solution: The LCM of 84 and 118 is 4956
Methods
How to find the LCM of 84 and 118 using Prime Factorization
One way to find the LCM of 84 and 118 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 118?
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 118:
2
1
×
5
9
1
2^1 × 59^1
2 1 × 5 9 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, 59
2
2
×
3
1
×
7
1
×
5
9
1
=
4956
2^2 × 3^1 × 7^1 × 59^1 = 4956
2 2 × 3 1 × 7 1 × 5 9 1 = 4956
Through this we see that the LCM of 84 and 118 is 4956.
How to Find the LCM of 84 and 118 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 84 and 118 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 118:
What are the Multiples of 84?
What are the Multiples of 118?
Let’s take a look at the first 10 multiples for each of these numbers, 84 and 118:
First 10 Multiples of 84: 84, 168, 252, 336, 420, 504, 588, 672, 756, 840
First 10 Multiples of 118: 118, 236, 354, 472, 590, 708, 826, 944, 1062, 1180
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 118 are 4956, 9912, 14868. Because 4956 is the smallest, it is the least common multiple.
The LCM of 84 and 118 is 4956.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 121 and 147?
What is the LCM of 14 and 91?
What is the LCM of 119 and 98?
What is the LCM of 3 and 145?
What is the LCM of 19 and 127?