Math Tutor Explains: What is the LCM of 150 and 34?

As your math tutor, I'm here to guide you through this problem! To find the LCM of 150 and 34, one effective method is comparing their prime factorizations. Start by breaking each number down into its prime factors. Follow these steps to determine the prime factorization of each number:

• What are the Factors of 150?
• What are the Factors of 34?

Here is the prime factorization of 150:

And this is the prime factorization of 34:

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, 17

Through this we see that the LCM of 150 and 34 is 2550.

The first step to this method of finding the Least Common Multiple of 150 and 34 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, 150 and 34:

What are the Multiples of 150?

What are the Multiples of 34?

Let’s take a look at the first 10 multiples for each of these numbers, 150 and 34:

First 10 Multiples of 150: 150, 300, 450, 600, 750, 900, 1050, 1200, 1350, 1500

First 10 Multiples of 34: 34, 68, 102, 136, 170, 204, 238, 272, 306, 340

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 150 and 34 are 2550, 5100, 7650. Because 2550 is the smallest, it is the least common multiple.

The LCM of 150 and 34 is 2550.

Want more practice? As a math tutor, I encourage you to try some of these other LCM problems:

• What is the LCM of 19 and 130?
• What is the LCM of 9 and 136?
• What is the LCM of 44 and 16?
• What is the LCM of 78 and 61?
• What is the LCM of 89 and 62?