Solution: The LCM of 24 and 149 is 3576
Methods
How to find the LCM of 24 and 149 using Prime Factorization
One way to find the LCM of 24 and 149 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 24?
What are the Factors of 149?
Here is the prime factorization of 24:
2
3
×
3
1
2^3 × 3^1
2 3 × 3 1
And this is the prime factorization of 149:
14
9
1
149^1
14 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, 149
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 24 and 149 is 3576.
How to Find the LCM of 24 and 149 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 24 and 149 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, 24 and 149:
What are the Multiples of 24?
What are the Multiples of 149?
Let’s take a look at the first 10 multiples for each of these numbers, 24 and 149:
First 10 Multiples of 24: 24, 48, 72, 96, 120, 144, 168, 192, 216, 240
First 10 Multiples of 149: 149, 298, 447, 596, 745, 894, 1043, 1192, 1341, 1490
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 24 and 149 are 3576, 7152, 10728. Because 3576 is the smallest, it is the least common multiple.
The LCM of 24 and 149 is 3576.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 74 and 145?
What is the LCM of 67 and 94?
What is the LCM of 150 and 136?
What is the LCM of 56 and 149?
What is the LCM of 33 and 77?