Solution: The LCM of 140 and 35 is 140
Methods
How to find the LCM of 140 and 35 using Prime Factorization
One way to find the LCM of 140 and 35 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 35?
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 35:
5
1
×
7
1
5^1 × 7^1
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, 5, 7
2
2
×
5
1
×
7
1
=
140
2^2 × 5^1 × 7^1 = 140
2 2 × 5 1 × 7 1 = 140
Through this we see that the LCM of 140 and 35 is 140.
How to Find the LCM of 140 and 35 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 140 and 35 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 35:
What are the Multiples of 140?
What are the Multiples of 35?
Let’s take a look at the first 10 multiples for each of these numbers, 140 and 35:
First 10 Multiples of 140: 140, 280, 420, 560, 700, 840, 980, 1120, 1260, 1400
First 10 Multiples of 35: 35, 70, 105, 140, 175, 210, 245, 280, 315, 350
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 35 are 140, 280, 420. Because 140 is the smallest, it is the least common multiple.
The LCM of 140 and 35 is 140.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 38 and 12?
What is the LCM of 9 and 132?
What is the LCM of 62 and 91?
What is the LCM of 59 and 43?
What is the LCM of 41 and 74?