Solution: The LCM of 34 and 104 is 1768
Methods
How to find the LCM of 34 and 104 using Prime Factorization
One way to find the LCM of 34 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 34?
What are the Factors of 104?
Here is the prime factorization of 34:
2
1
×
1
7
1
2^1 × 17^1
2 1 × 1 7 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: 2, 17, 13
2
3
×
1
3
1
×
1
7
1
=
1768
2^3 × 13^1 × 17^1 = 1768
2 3 × 1 3 1 × 1 7 1 = 1768
Through this we see that the LCM of 34 and 104 is 1768.
How to Find the LCM of 34 and 104 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 34 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, 34 and 104:
What are the Multiples of 34?
What are the Multiples of 104?
Let’s take a look at the first 10 multiples for each of these numbers, 34 and 104:
First 10 Multiples of 34: 34, 68, 102, 136, 170, 204, 238, 272, 306, 340
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 34 and 104 are 1768, 3536, 5304. Because 1768 is the smallest, it is the least common multiple.
The LCM of 34 and 104 is 1768.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 24 and 13?
What is the LCM of 23 and 135?
What is the LCM of 91 and 33?
What is the LCM of 1 and 43?
What is the LCM of 100 and 42?