Solution: The LCM of 78 and 129 is 3354
Methods
How to find the LCM of 78 and 129 using Prime Factorization
One way to find the LCM of 78 and 129 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 78?
What are the Factors of 129?
Here is the prime factorization of 78:
2
1
×
3
1
×
1
3
1
2^1 × 3^1 × 13^1
2 1 × 3 1 × 1 3 1
And this is the prime factorization of 129:
3
1
×
4
3
1
3^1 × 43^1
3 1 × 4 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: 2, 3, 13, 43
2
1
×
3
1
×
1
3
1
×
4
3
1
=
3354
2^1 × 3^1 × 13^1 × 43^1 = 3354
2 1 × 3 1 × 1 3 1 × 4 3 1 = 3354
Through this we see that the LCM of 78 and 129 is 3354.
How to Find the LCM of 78 and 129 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 78 and 129 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, 78 and 129:
What are the Multiples of 78?
What are the Multiples of 129?
Let’s take a look at the first 10 multiples for each of these numbers, 78 and 129:
First 10 Multiples of 78: 78, 156, 234, 312, 390, 468, 546, 624, 702, 780
First 10 Multiples of 129: 129, 258, 387, 516, 645, 774, 903, 1032, 1161, 1290
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 78 and 129 are 3354, 6708, 10062. Because 3354 is the smallest, it is the least common multiple.
The LCM of 78 and 129 is 3354.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 62 and 59?
What is the LCM of 74 and 102?
What is the LCM of 38 and 133?
What is the LCM of 114 and 104?
What is the LCM of 108 and 28?