Solution: The LCM of 138 and 71 is 9798
Methods
How to find the LCM of 138 and 71 using Prime Factorization
One way to find the LCM of 138 and 71 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 138?
What are the Factors of 71?
Here is the prime factorization of 138:
2
1
×
3
1
×
2
3
1
2^1 × 3^1 × 23^1
2 1 × 3 1 × 2 3 1
And this is the prime factorization of 71:
7
1
1
71^1
7 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, 3, 23, 71
2
1
×
3
1
×
2
3
1
×
7
1
1
=
9798
2^1 × 3^1 × 23^1 × 71^1 = 9798
2 1 × 3 1 × 2 3 1 × 7 1 1 = 9798
Through this we see that the LCM of 138 and 71 is 9798.
How to Find the LCM of 138 and 71 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 138 and 71 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, 138 and 71:
What are the Multiples of 138?
What are the Multiples of 71?
Let’s take a look at the first 10 multiples for each of these numbers, 138 and 71:
First 10 Multiples of 138: 138, 276, 414, 552, 690, 828, 966, 1104, 1242, 1380
First 10 Multiples of 71: 71, 142, 213, 284, 355, 426, 497, 568, 639, 710
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 138 and 71 are 9798, 19596, 29394. Because 9798 is the smallest, it is the least common multiple.
The LCM of 138 and 71 is 9798.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 54 and 86?
What is the LCM of 126 and 121?
What is the LCM of 40 and 141?
What is the LCM of 66 and 140?
What is the LCM of 49 and 91?