Solution: The LCM of 33 and 147 is 1617
Methods
How to find the LCM of 33 and 147 using Prime Factorization
One way to find the LCM of 33 and 147 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 33?
What are the Factors of 147?
Here is the prime factorization of 33:
3
1
×
1
1
1
3^1 × 11^1
3 1 × 1 1 1
And this is the prime factorization of 147:
3
1
×
7
2
3^1 × 7^2
3 1 × 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, 11, 7
3
1
×
7
2
×
1
1
1
=
1617
3^1 × 7^2 × 11^1 = 1617
3 1 × 7 2 × 1 1 1 = 1617
Through this we see that the LCM of 33 and 147 is 1617.
How to Find the LCM of 33 and 147 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 33 and 147 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, 33 and 147:
What are the Multiples of 33?
What are the Multiples of 147?
Let’s take a look at the first 10 multiples for each of these numbers, 33 and 147:
First 10 Multiples of 33: 33, 66, 99, 132, 165, 198, 231, 264, 297, 330
First 10 Multiples of 147: 147, 294, 441, 588, 735, 882, 1029, 1176, 1323, 1470
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 33 and 147 are 1617, 3234, 4851. Because 1617 is the smallest, it is the least common multiple.
The LCM of 33 and 147 is 1617.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 7 and 36?
What is the LCM of 117 and 78?
What is the LCM of 81 and 68?
What is the LCM of 70 and 27?
What is the LCM of 72 and 123?