Solution: The LCM of 59 and 30 is 1770
Methods
How to find the LCM of 59 and 30 using Prime Factorization
One way to find the LCM of 59 and 30 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 59?
What are the Factors of 30?
Here is the prime factorization of 59:
5
9
1
59^1
5 9 1
And this is the prime factorization of 30:
2
1
×
3
1
×
5
1
2^1 × 3^1 × 5^1
2 1 × 3 1 × 5 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: 59, 2, 3, 5
2
1
×
3
1
×
5
1
×
5
9
1
=
1770
2^1 × 3^1 × 5^1 × 59^1 = 1770
2 1 × 3 1 × 5 1 × 5 9 1 = 1770
Through this we see that the LCM of 59 and 30 is 1770.
How to Find the LCM of 59 and 30 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 59 and 30 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, 59 and 30:
What are the Multiples of 59?
What are the Multiples of 30?
Let’s take a look at the first 10 multiples for each of these numbers, 59 and 30:
First 10 Multiples of 59: 59, 118, 177, 236, 295, 354, 413, 472, 531, 590
First 10 Multiples of 30: 30, 60, 90, 120, 150, 180, 210, 240, 270, 300
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 59 and 30 are 1770, 3540, 5310. Because 1770 is the smallest, it is the least common multiple.
The LCM of 59 and 30 is 1770.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 120 and 17?
What is the LCM of 40 and 60?
What is the LCM of 67 and 11?
What is the LCM of 36 and 99?
What is the LCM of 31 and 136?