Solution: The LCM of 137 and 23 is 3151
Methods
How to find the LCM of 137 and 23 using Prime Factorization
One way to find the LCM of 137 and 23 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 137?
What are the Factors of 23?
Here is the prime factorization of 137:
13
7
1
137^1
13 7 1
And this is the prime factorization of 23:
2
3
1
23^1
2 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: 137, 23
2
3
1
×
13
7
1
=
3151
23^1 × 137^1 = 3151
2 3 1 × 13 7 1 = 3151
Through this we see that the LCM of 137 and 23 is 3151.
How to Find the LCM of 137 and 23 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 137 and 23 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, 137 and 23:
What are the Multiples of 137?
What are the Multiples of 23?
Let’s take a look at the first 10 multiples for each of these numbers, 137 and 23:
First 10 Multiples of 137: 137, 274, 411, 548, 685, 822, 959, 1096, 1233, 1370
First 10 Multiples of 23: 23, 46, 69, 92, 115, 138, 161, 184, 207, 230
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 137 and 23 are 3151, 6302, 9453. Because 3151 is the smallest, it is the least common multiple.
The LCM of 137 and 23 is 3151.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 14 and 132?
What is the LCM of 91 and 104?
What is the LCM of 140 and 37?
What is the LCM of 92 and 76?
What is the LCM of 145 and 45?