Solution: The LCM of 30 and 42 is 210
Methods
How to find the LCM of 30 and 42 using Prime Factorization
One way to find the LCM of 30 and 42 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 42?
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 42:
2
1
×
3
1
×
7
1
2^1 × 3^1 × 7^1
2 1 × 3 1 × 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, 7
2
1
×
3
1
×
5
1
×
7
1
=
210
2^1 × 3^1 × 5^1 × 7^1 = 210
2 1 × 3 1 × 5 1 × 7 1 = 210
Through this we see that the LCM of 30 and 42 is 210.
How to Find the LCM of 30 and 42 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 30 and 42 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 42:
What are the Multiples of 30?
What are the Multiples of 42?
Let’s take a look at the first 10 multiples for each of these numbers, 30 and 42:
First 10 Multiples of 30: 30, 60, 90, 120, 150, 180, 210, 240, 270, 300
First 10 Multiples of 42: 42, 84, 126, 168, 210, 252, 294, 336, 378, 420
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 42 are 210, 420, 630. Because 210 is the smallest, it is the least common multiple.
The LCM of 30 and 42 is 210.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 9 and 145?
What is the LCM of 88 and 45?
What is the LCM of 140 and 121?
What is the LCM of 124 and 110?
What is the LCM of 2 and 104?