Solution: The LCM of 131 and 113 is 14803
Methods
How to find the LCM of 131 and 113 using Prime Factorization
One way to find the LCM of 131 and 113 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 131?
What are the Factors of 113?
Here is the prime factorization of 131:
13
1
1
131^1
13 1 1
And this is the prime factorization of 113:
11
3
1
113^1
11 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: 131, 113
11
3
1
×
13
1
1
=
14803
113^1 × 131^1 = 14803
11 3 1 × 13 1 1 = 14803
Through this we see that the LCM of 131 and 113 is 14803.
How to Find the LCM of 131 and 113 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 131 and 113 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, 131 and 113:
What are the Multiples of 131?
What are the Multiples of 113?
Let’s take a look at the first 10 multiples for each of these numbers, 131 and 113:
First 10 Multiples of 131: 131, 262, 393, 524, 655, 786, 917, 1048, 1179, 1310
First 10 Multiples of 113: 113, 226, 339, 452, 565, 678, 791, 904, 1017, 1130
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 131 and 113 are 14803, 29606, 44409. Because 14803 is the smallest, it is the least common multiple.
The LCM of 131 and 113 is 14803.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 41 and 58?
What is the LCM of 116 and 36?
What is the LCM of 78 and 77?
What is the LCM of 69 and 143?
What is the LCM of 136 and 121?