Solution: The LCM of 30 and 67 is 2010
Methods
How to find the LCM of 30 and 67 using Prime Factorization
One way to find the LCM of 30 and 67 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 30?
What are the Factors of 67?
Here is the prime factorization of 30:
2
1
×
3
1
×
5
1
2^1 × 3^1 × 5^1
2 1 × 3 1 × 5 1
And this is the prime factorization of 67:
6
7
1
67^1
6 7 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, 5, 67
2
1
×
3
1
×
5
1
×
6
7
1
=
2010
2^1 × 3^1 × 5^1 × 67^1 = 2010
2 1 × 3 1 × 5 1 × 6 7 1 = 2010
Through this we see that the LCM of 30 and 67 is 2010.
How to Find the LCM of 30 and 67 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 30 and 67 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, 30 and 67:
What are the Multiples of 30?
What are the Multiples of 67?
Let’s take a look at the first 10 multiples for each of these numbers, 30 and 67:
First 10 Multiples of 30: 30, 60, 90, 120, 150, 180, 210, 240, 270, 300
First 10 Multiples of 67: 67, 134, 201, 268, 335, 402, 469, 536, 603, 670
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 30 and 67 are 2010, 4020, 6030. Because 2010 is the smallest, it is the least common multiple.
The LCM of 30 and 67 is 2010.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 98 and 68?
What is the LCM of 124 and 86?
What is the LCM of 67 and 96?
What is the LCM of 74 and 108?
What is the LCM of 95 and 32?