Solution: The LCM of 138 and 5 is 690
Methods
How to find the LCM of 138 and 5 using Prime Factorization
One way to find the LCM of 138 and 5 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 5?
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 5:
5
1
5^1
5 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, 5
2
1
×
3
1
×
5
1
×
2
3
1
=
690
2^1 × 3^1 × 5^1 × 23^1 = 690
2 1 × 3 1 × 5 1 × 2 3 1 = 690
Through this we see that the LCM of 138 and 5 is 690.
How to Find the LCM of 138 and 5 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 138 and 5 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 5:
What are the Multiples of 138?
What are the Multiples of 5?
Let’s take a look at the first 10 multiples for each of these numbers, 138 and 5:
First 10 Multiples of 138: 138, 276, 414, 552, 690, 828, 966, 1104, 1242, 1380
First 10 Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50
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 5 are 690, 1380, 2070. Because 690 is the smallest, it is the least common multiple.
The LCM of 138 and 5 is 690.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 122 and 93?
What is the LCM of 118 and 144?
What is the LCM of 82 and 55?
What is the LCM of 115 and 134?
What is the LCM of 20 and 26?