Solution: The LCM of 30 and 148 is 2220
Methods
How to find the LCM of 30 and 148 using Prime Factorization
One way to find the LCM of 30 and 148 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 148?
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 148:
2
2
×
3
7
1
2^2 × 37^1
2 2 × 3 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, 37
2
2
×
3
1
×
5
1
×
3
7
1
=
2220
2^2 × 3^1 × 5^1 × 37^1 = 2220
2 2 × 3 1 × 5 1 × 3 7 1 = 2220
Through this we see that the LCM of 30 and 148 is 2220.
How to Find the LCM of 30 and 148 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 30 and 148 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 148:
What are the Multiples of 30?
What are the Multiples of 148?
Let’s take a look at the first 10 multiples for each of these numbers, 30 and 148:
First 10 Multiples of 30: 30, 60, 90, 120, 150, 180, 210, 240, 270, 300
First 10 Multiples of 148: 148, 296, 444, 592, 740, 888, 1036, 1184, 1332, 1480
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 148 are 2220, 4440, 6660. Because 2220 is the smallest, it is the least common multiple.
The LCM of 30 and 148 is 2220.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 70 and 136?
What is the LCM of 128 and 23?
What is the LCM of 89 and 65?
What is the LCM of 37 and 104?
What is the LCM of 137 and 57?