Solution: The LCM of 129 and 104 is 13416
Methods
How to find the LCM of 129 and 104 using Prime Factorization
One way to find the LCM of 129 and 104 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 104?
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 104:
2
3
×
1
3
1
2^3 × 13^1
2 3 × 1 3 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, 13
2
3
×
3
1
×
1
3
1
×
4
3
1
=
13416
2^3 × 3^1 × 13^1 × 43^1 = 13416
2 3 × 3 1 × 1 3 1 × 4 3 1 = 13416
Through this we see that the LCM of 129 and 104 is 13416.
How to Find the LCM of 129 and 104 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 129 and 104 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 104:
What are the Multiples of 129?
What are the Multiples of 104?
Let’s take a look at the first 10 multiples for each of these numbers, 129 and 104:
First 10 Multiples of 129: 129, 258, 387, 516, 645, 774, 903, 1032, 1161, 1290
First 10 Multiples of 104: 104, 208, 312, 416, 520, 624, 728, 832, 936, 1040
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 104 are 13416, 26832, 40248. Because 13416 is the smallest, it is the least common multiple.
The LCM of 129 and 104 is 13416.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 80 and 37?
What is the LCM of 141 and 99?
What is the LCM of 89 and 14?
What is the LCM of 100 and 61?
What is the LCM of 53 and 83?