Solution: The LCM of 149 and 60 is 8940
Methods
How to find the LCM of 149 and 60 using Prime Factorization
One way to find the LCM of 149 and 60 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 149?
What are the Factors of 60?
Here is the prime factorization of 149:
14
9
1
149^1
14 9 1
And this is the prime factorization of 60:
2
2
×
3
1
×
5
1
2^2 × 3^1 × 5^1
2 2 × 3 1 × 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: 149, 2, 3, 5
2
2
×
3
1
×
5
1
×
14
9
1
=
8940
2^2 × 3^1 × 5^1 × 149^1 = 8940
2 2 × 3 1 × 5 1 × 14 9 1 = 8940
Through this we see that the LCM of 149 and 60 is 8940.
How to Find the LCM of 149 and 60 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 149 and 60 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, 149 and 60:
What are the Multiples of 149?
What are the Multiples of 60?
Let’s take a look at the first 10 multiples for each of these numbers, 149 and 60:
First 10 Multiples of 149: 149, 298, 447, 596, 745, 894, 1043, 1192, 1341, 1490
First 10 Multiples of 60: 60, 120, 180, 240, 300, 360, 420, 480, 540, 600
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 149 and 60 are 8940, 17880, 26820. Because 8940 is the smallest, it is the least common multiple.
The LCM of 149 and 60 is 8940.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 40 and 144?
What is the LCM of 34 and 43?
What is the LCM of 146 and 32?
What is the LCM of 8 and 36?
What is the LCM of 4 and 15?