Solution: The LCM of 149 and 52 is 7748
Methods
How to find the LCM of 149 and 52 using Prime Factorization
One way to find the LCM of 149 and 52 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 52?
Here is the prime factorization of 149:
14
9
1
149^1
14 9 1
And this is the prime factorization of 52:
2
2
×
1
3
1
2^2 × 13^1
2 2 × 1 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, 13
2
2
×
1
3
1
×
14
9
1
=
7748
2^2 × 13^1 × 149^1 = 7748
2 2 × 1 3 1 × 14 9 1 = 7748
Through this we see that the LCM of 149 and 52 is 7748.
How to Find the LCM of 149 and 52 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 149 and 52 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 52:
What are the Multiples of 149?
What are the Multiples of 52?
Let’s take a look at the first 10 multiples for each of these numbers, 149 and 52:
First 10 Multiples of 149: 149, 298, 447, 596, 745, 894, 1043, 1192, 1341, 1490
First 10 Multiples of 52: 52, 104, 156, 208, 260, 312, 364, 416, 468, 520
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 52 are 7748, 15496, 23244. Because 7748 is the smallest, it is the least common multiple.
The LCM of 149 and 52 is 7748.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 7 and 35?
What is the LCM of 37 and 20?
What is the LCM of 5 and 76?
What is the LCM of 26 and 13?
What is the LCM of 50 and 96?