Solution: The LCM of 129 and 40 is 5160
Methods
How to find the LCM of 129 and 40 using Prime Factorization
One way to find the LCM of 129 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 129?
What are the Factors of 40?
Here is the prime factorization of 129:
3
1
×
4
3
1
3^1 × 43^1
3 1 × 4 3 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: 3, 43, 2, 5
2
3
×
3
1
×
5
1
×
4
3
1
=
5160
2^3 × 3^1 × 5^1 × 43^1 = 5160
2 3 × 3 1 × 5 1 × 4 3 1 = 5160
Through this we see that the LCM of 129 and 40 is 5160.
How to Find the LCM of 129 and 40 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 129 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, 129 and 40:
What are the Multiples of 129?
What are the Multiples of 40?
Let’s take a look at the first 10 multiples for each of these numbers, 129 and 40:
First 10 Multiples of 129: 129, 258, 387, 516, 645, 774, 903, 1032, 1161, 1290
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 129 and 40 are 5160, 10320, 15480. Because 5160 is the smallest, it is the least common multiple.
The LCM of 129 and 40 is 5160.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 112 and 42?
What is the LCM of 124 and 20?
What is the LCM of 50 and 91?
What is the LCM of 28 and 134?
What is the LCM of 1 and 99?