Solution: The LCM of 40 and 35 is 280
Methods
How to find the LCM of 40 and 35 using Prime Factorization
One way to find the LCM of 40 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 40?
What are the Factors of 35?
Here is the prime factorization of 40:
2
3
×
5
1
2^3 × 5^1
2 3 × 5 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
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 40 and 35 is 280.
How to Find the LCM of 40 and 35 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 40 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, 40 and 35:
What are the Multiples of 40?
What are the Multiples of 35?
Let’s take a look at the first 10 multiples for each of these numbers, 40 and 35:
First 10 Multiples of 40: 40, 80, 120, 160, 200, 240, 280, 320, 360, 400
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 40 and 35 are 280, 560, 840. Because 280 is the smallest, it is the least common multiple.
The LCM of 40 and 35 is 280.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 129 and 146?
What is the LCM of 33 and 118?
What is the LCM of 113 and 128?
What is the LCM of 92 and 105?
What is the LCM of 51 and 64?