Solution: The LCM of 104 and 33 is 3432
Methods
How to find the LCM of 104 and 33 using Prime Factorization
One way to find the LCM of 104 and 33 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 104?
What are the Factors of 33?
Here is the prime factorization of 104:
2
3
×
1
3
1
2^3 × 13^1
2 3 × 1 3 1
And this is the prime factorization of 33:
3
1
×
1
1
1
3^1 × 11^1
3 1 × 1 1 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, 13, 3, 11
2
3
×
3
1
×
1
1
1
×
1
3
1
=
3432
2^3 × 3^1 × 11^1 × 13^1 = 3432
2 3 × 3 1 × 1 1 1 × 1 3 1 = 3432
Through this we see that the LCM of 104 and 33 is 3432.
How to Find the LCM of 104 and 33 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 104 and 33 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, 104 and 33:
What are the Multiples of 104?
What are the Multiples of 33?
Let’s take a look at the first 10 multiples for each of these numbers, 104 and 33:
First 10 Multiples of 104: 104, 208, 312, 416, 520, 624, 728, 832, 936, 1040
First 10 Multiples of 33: 33, 66, 99, 132, 165, 198, 231, 264, 297, 330
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 104 and 33 are 3432, 6864, 10296. Because 3432 is the smallest, it is the least common multiple.
The LCM of 104 and 33 is 3432.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 51 and 124?
What is the LCM of 55 and 126?
What is the LCM of 101 and 48?
What is the LCM of 52 and 68?
What is the LCM of 40 and 115?