Solution: The LCM of 146 and 84 is 6132
Methods
How to find the LCM of 146 and 84 using Prime Factorization
One way to find the LCM of 146 and 84 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 146?
What are the Factors of 84?
Here is the prime factorization of 146:
2
1
×
7
3
1
2^1 × 73^1
2 1 × 7 3 1
And this is the prime factorization of 84:
2
2
×
3
1
×
7
1
2^2 × 3^1 × 7^1
2 2 × 3 1 × 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, 73, 3, 7
2
2
×
3
1
×
7
1
×
7
3
1
=
6132
2^2 × 3^1 × 7^1 × 73^1 = 6132
2 2 × 3 1 × 7 1 × 7 3 1 = 6132
Through this we see that the LCM of 146 and 84 is 6132.
How to Find the LCM of 146 and 84 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 146 and 84 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, 146 and 84:
What are the Multiples of 146?
What are the Multiples of 84?
Let’s take a look at the first 10 multiples for each of these numbers, 146 and 84:
First 10 Multiples of 146: 146, 292, 438, 584, 730, 876, 1022, 1168, 1314, 1460
First 10 Multiples of 84: 84, 168, 252, 336, 420, 504, 588, 672, 756, 840
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 146 and 84 are 6132, 12264, 18396. Because 6132 is the smallest, it is the least common multiple.
The LCM of 146 and 84 is 6132.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 78 and 24?
What is the LCM of 90 and 98?
What is the LCM of 144 and 42?
What is the LCM of 6 and 4?
What is the LCM of 1 and 75?