Solution: The LCM of 134 and 131 is 17554
Methods
How to find the LCM of 134 and 131 using Prime Factorization
One way to find the LCM of 134 and 131 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 134?
What are the Factors of 131?
Here is the prime factorization of 134:
2
1
×
6
7
1
2^1 × 67^1
2 1 × 6 7 1
And this is the prime factorization of 131:
13
1
1
131^1
13 1 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: 2, 67, 131
2
1
×
6
7
1
×
13
1
1
=
17554
2^1 × 67^1 × 131^1 = 17554
2 1 × 6 7 1 × 13 1 1 = 17554
Through this we see that the LCM of 134 and 131 is 17554.
How to Find the LCM of 134 and 131 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 134 and 131 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, 134 and 131:
What are the Multiples of 134?
What are the Multiples of 131?
Let’s take a look at the first 10 multiples for each of these numbers, 134 and 131:
First 10 Multiples of 134: 134, 268, 402, 536, 670, 804, 938, 1072, 1206, 1340
First 10 Multiples of 131: 131, 262, 393, 524, 655, 786, 917, 1048, 1179, 1310
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 134 and 131 are 17554, 35108, 52662. Because 17554 is the smallest, it is the least common multiple.
The LCM of 134 and 131 is 17554.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 53 and 103?
What is the LCM of 15 and 113?
What is the LCM of 142 and 33?
What is the LCM of 123 and 106?
What is the LCM of 105 and 41?