Solution: The LCM of 129 and 49 is 6321
Methods
How to find the LCM of 129 and 49 using Prime Factorization
One way to find the LCM of 129 and 49 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 49?
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 49:
7
2
7^2
7 2
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, 7
3
1
×
7
2
×
4
3
1
=
6321
3^1 × 7^2 × 43^1 = 6321
3 1 × 7 2 × 4 3 1 = 6321
Through this we see that the LCM of 129 and 49 is 6321.
How to Find the LCM of 129 and 49 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 129 and 49 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 49:
What are the Multiples of 129?
What are the Multiples of 49?
Let’s take a look at the first 10 multiples for each of these numbers, 129 and 49:
First 10 Multiples of 129: 129, 258, 387, 516, 645, 774, 903, 1032, 1161, 1290
First 10 Multiples of 49: 49, 98, 147, 196, 245, 294, 343, 392, 441, 490
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 49 are 6321, 12642, 18963. Because 6321 is the smallest, it is the least common multiple.
The LCM of 129 and 49 is 6321.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 53 and 96?
What is the LCM of 27 and 91?
What is the LCM of 11 and 13?
What is the LCM of 135 and 49?
What is the LCM of 52 and 61?