Solution: The LCM of 140 and 8 is 280
Methods
How to find the LCM of 140 and 8 using Prime Factorization
One way to find the LCM of 140 and 8 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 140?
What are the Factors of 8?
Here is the prime factorization of 140:
2
2
×
5
1
×
7
1
2^2 × 5^1 × 7^1
2 2 × 5 1 × 7 1
And this is the prime factorization of 8:
2
3
2^3
2 3
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, 5, 7
2
3
×
5
1
×
7
1
=
280
2^3 × 5^1 × 7^1 = 280
2 3 × 5 1 × 7 1 = 280
Through this we see that the LCM of 140 and 8 is 280.
How to Find the LCM of 140 and 8 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 140 and 8 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, 140 and 8:
What are the Multiples of 140?
What are the Multiples of 8?
Let’s take a look at the first 10 multiples for each of these numbers, 140 and 8:
First 10 Multiples of 140: 140, 280, 420, 560, 700, 840, 980, 1120, 1260, 1400
First 10 Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80
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 140 and 8 are 280, 560, 840. Because 280 is the smallest, it is the least common multiple.
The LCM of 140 and 8 is 280.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 136 and 56?
What is the LCM of 104 and 87?
What is the LCM of 61 and 47?
What is the LCM of 128 and 138?
What is the LCM of 53 and 144?