Solution: The LCM of 29 and 40 is 1160
Methods
How to find the LCM of 29 and 40 using Prime Factorization
One way to find the LCM of 29 and 40 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 29?
What are the Factors of 40?
Here is the prime factorization of 29:
2
9
1
29^1
2 9 1
And this is the prime factorization of 40:
2
3
×
5
1
2^3 × 5^1
2 3 × 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: 29, 2, 5
2
3
×
5
1
×
2
9
1
=
1160
2^3 × 5^1 × 29^1 = 1160
2 3 × 5 1 × 2 9 1 = 1160
Through this we see that the LCM of 29 and 40 is 1160.
How to Find the LCM of 29 and 40 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 29 and 40 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, 29 and 40:
What are the Multiples of 29?
What are the Multiples of 40?
Let’s take a look at the first 10 multiples for each of these numbers, 29 and 40:
First 10 Multiples of 29: 29, 58, 87, 116, 145, 174, 203, 232, 261, 290
First 10 Multiples of 40: 40, 80, 120, 160, 200, 240, 280, 320, 360, 400
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 29 and 40 are 1160, 2320, 3480. Because 1160 is the smallest, it is the least common multiple.
The LCM of 29 and 40 is 1160.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 47 and 101?
What is the LCM of 53 and 11?
What is the LCM of 64 and 129?
What is the LCM of 118 and 69?
What is the LCM of 150 and 30?