Solution: The LCM of 30 and 74 is 1110
Methods
How to find the LCM of 30 and 74 using Prime Factorization
One way to find the LCM of 30 and 74 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 74?
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 74:
2
1
×
3
7
1
2^1 × 37^1
2 1 × 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
1
×
3
1
×
5
1
×
3
7
1
=
1110
2^1 × 3^1 × 5^1 × 37^1 = 1110
2 1 × 3 1 × 5 1 × 3 7 1 = 1110
Through this we see that the LCM of 30 and 74 is 1110.
How to Find the LCM of 30 and 74 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 30 and 74 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 74:
What are the Multiples of 30?
What are the Multiples of 74?
Let’s take a look at the first 10 multiples for each of these numbers, 30 and 74:
First 10 Multiples of 30: 30, 60, 90, 120, 150, 180, 210, 240, 270, 300
First 10 Multiples of 74: 74, 148, 222, 296, 370, 444, 518, 592, 666, 740
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 74 are 1110, 2220, 3330. Because 1110 is the smallest, it is the least common multiple.
The LCM of 30 and 74 is 1110.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 53 and 67?
What is the LCM of 33 and 122?
What is the LCM of 133 and 86?
What is the LCM of 107 and 6?
What is the LCM of 78 and 45?