Solution: The LCM of 60 and 140 is 420
Methods
How to find the LCM of 60 and 140 using Prime Factorization
One way to find the LCM of 60 and 140 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 60?
What are the Factors of 140?
Here is the prime factorization of 60:
2
2
×
3
1
×
5
1
2^2 × 3^1 × 5^1
2 2 × 3 1 × 5 1
And this is the prime factorization of 140:
2
2
×
5
1
×
7
1
2^2 × 5^1 × 7^1
2 2 × 5 1 × 7 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, 5, 7
2
2
×
3
1
×
5
1
×
7
1
=
420
2^2 × 3^1 × 5^1 × 7^1 = 420
2 2 × 3 1 × 5 1 × 7 1 = 420
Through this we see that the LCM of 60 and 140 is 420.
How to Find the LCM of 60 and 140 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 60 and 140 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, 60 and 140:
What are the Multiples of 60?
What are the Multiples of 140?
Let’s take a look at the first 10 multiples for each of these numbers, 60 and 140:
First 10 Multiples of 60: 60, 120, 180, 240, 300, 360, 420, 480, 540, 600
First 10 Multiples of 140: 140, 280, 420, 560, 700, 840, 980, 1120, 1260, 1400
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 60 and 140 are 420, 840, 1260. Because 420 is the smallest, it is the least common multiple.
The LCM of 60 and 140 is 420.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 130 and 146?
What is the LCM of 88 and 99?
What is the LCM of 36 and 82?
What is the LCM of 25 and 92?
What is the LCM of 125 and 22?