Solution: The LCM of 14 and 33 is 462
Methods
How to find the LCM of 14 and 33 using Prime Factorization
One way to find the LCM of 14 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 14?
What are the Factors of 33?
Here is the prime factorization of 14:
2
1
×
7
1
2^1 × 7^1
2 1 × 7 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, 7, 3, 11
2
1
×
3
1
×
7
1
×
1
1
1
=
462
2^1 × 3^1 × 7^1 × 11^1 = 462
2 1 × 3 1 × 7 1 × 1 1 1 = 462
Through this we see that the LCM of 14 and 33 is 462.
How to Find the LCM of 14 and 33 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 14 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, 14 and 33:
What are the Multiples of 14?
What are the Multiples of 33?
Let’s take a look at the first 10 multiples for each of these numbers, 14 and 33:
First 10 Multiples of 14: 14, 28, 42, 56, 70, 84, 98, 112, 126, 140
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 14 and 33 are 462, 924, 1386. Because 462 is the smallest, it is the least common multiple.
The LCM of 14 and 33 is 462.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 9 and 55?
What is the LCM of 102 and 6?
What is the LCM of 77 and 113?
What is the LCM of 137 and 142?
What is the LCM of 108 and 52?