Solution: The LCM of 149 and 24 is 3576
Methods
How to find the LCM of 149 and 24 using Prime Factorization
One way to find the LCM of 149 and 24 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 24?
Here is the prime factorization of 149:
14
9
1
149^1
14 9 1
And this is the prime factorization of 24:
2
3
×
3
1
2^3 × 3^1
2 3 × 3 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
2
3
×
3
1
×
14
9
1
=
3576
2^3 × 3^1 × 149^1 = 3576
2 3 × 3 1 × 14 9 1 = 3576
Through this we see that the LCM of 149 and 24 is 3576.
How to Find the LCM of 149 and 24 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 149 and 24 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 24:
What are the Multiples of 149?
What are the Multiples of 24?
Let’s take a look at the first 10 multiples for each of these numbers, 149 and 24:
First 10 Multiples of 149: 149, 298, 447, 596, 745, 894, 1043, 1192, 1341, 1490
First 10 Multiples of 24: 24, 48, 72, 96, 120, 144, 168, 192, 216, 240
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 24 are 3576, 7152, 10728. Because 3576 is the smallest, it is the least common multiple.
The LCM of 149 and 24 is 3576.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 139 and 18?
What is the LCM of 95 and 51?
What is the LCM of 92 and 68?
What is the LCM of 31 and 25?
What is the LCM of 17 and 9?