Solution: The LCM of 53 and 149 is 7897
Methods
How to find the LCM of 53 and 149 using Prime Factorization
One way to find the LCM of 53 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 53?
What are the Factors of 149?
Here is the prime factorization of 53:
5
3
1
53^1
5 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: 53, 149
5
3
1
×
14
9
1
=
7897
53^1 × 149^1 = 7897
5 3 1 × 14 9 1 = 7897
Through this we see that the LCM of 53 and 149 is 7897.
How to Find the LCM of 53 and 149 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 53 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, 53 and 149:
What are the Multiples of 53?
What are the Multiples of 149?
Let’s take a look at the first 10 multiples for each of these numbers, 53 and 149:
First 10 Multiples of 53: 53, 106, 159, 212, 265, 318, 371, 424, 477, 530
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 53 and 149 are 7897, 15794, 23691. Because 7897 is the smallest, it is the least common multiple.
The LCM of 53 and 149 is 7897.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 33 and 25?
What is the LCM of 149 and 99?
What is the LCM of 55 and 76?
What is the LCM of 48 and 91?
What is the LCM of 119 and 140?