What is the LCM of 30 and 89?

Solution: The LCM of 30 and 89 is 2670

Methods

How to find the LCM of 30 and 89 using Prime Factorization

One way to find the LCM of 30 and 89 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:

Here is the prime factorization of 30:

2^1 × 3^1 × 5^1

And this is the prime factorization of 89:

89^1

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, 89

2^1 × 3^1 × 5^1 × 89^1 = 2670

Through this we see that the LCM of 30 and 89 is 2670.

How to Find the LCM of 30 and 89 by Listing Common Multiples

The first step to this method of finding the Least Common Multiple of 30 and 89 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 89:

What are the Multiples of 30?

What are the Multiples of 89?

Let’s take a look at the first 10 multiples for each of these numbers, 30 and 89:

First 10 Multiples of 30: 30, 60, 90, 120, 150, 180, 210, 240, 270, 300

First 10 Multiples of 89: 89, 178, 267, 356, 445, 534, 623, 712, 801, 890

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 89 are 2670, 5340, 8010. Because 2670 is the smallest, it is the least common multiple.

The LCM of 30 and 89 is 2670.

Find the LCM of Other Number Pairs

Want more practice? Try some of these other LCM problems:

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