Solution: The LCM of 81 and 137 is 11097
Methods
How to find the LCM of 81 and 137 using Prime Factorization
One way to find the LCM of 81 and 137 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 81?
What are the Factors of 137?
Here is the prime factorization of 81:
3
4
3^4
3 4
And this is the prime factorization of 137:
13
7
1
137^1
13 7 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: 3, 137
3
4
×
13
7
1
=
11097
3^4 × 137^1 = 11097
3 4 × 13 7 1 = 11097
Through this we see that the LCM of 81 and 137 is 11097.
How to Find the LCM of 81 and 137 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 81 and 137 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, 81 and 137:
What are the Multiples of 81?
What are the Multiples of 137?
Let’s take a look at the first 10 multiples for each of these numbers, 81 and 137:
First 10 Multiples of 81: 81, 162, 243, 324, 405, 486, 567, 648, 729, 810
First 10 Multiples of 137: 137, 274, 411, 548, 685, 822, 959, 1096, 1233, 1370
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 81 and 137 are 11097, 22194, 33291. Because 11097 is the smallest, it is the least common multiple.
The LCM of 81 and 137 is 11097.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 45 and 57?
What is the LCM of 2 and 143?
What is the LCM of 39 and 76?
What is the LCM of 63 and 16?
What is the LCM of 91 and 139?