Math Tutor Explains: What is the LCM of 146 and 106?

Your math tutor is here to explain! The Least Common Multiple (LCM) of two or more numbers is the smallest number that all the given numbers can divide into evenly. In other words, the LCM of 146 and 106 is the smallest value that both 146 and 106 can divide exactly, without leaving a remainder. Let’s explore how to find it!

Math Tutor Solution: The LCM of 146 and 106 is 7738

Methods

How to find the LCM of 146 and 106 using Prime Factorization

As your math tutor, I'm here to guide you through this problem! To find the LCM of 146 and 106, 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:

Here is the prime factorization of 146:

21×7312^1 × 73^1

And this is the prime factorization of 106:

21×5312^1 × 53^1

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, 73, 53

21×531×731=77382^1 × 53^1 × 73^1 = 7738

Through this we see that the LCM of 146 and 106 is 7738.

How to Find the LCM of 146 and 106 by Listing Common Multiples

The first step to this method of finding the Least Common Multiple of 146 and 106 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, 146 and 106:

What are the Multiples of 146?

What are the Multiples of 106?

Let’s take a look at the first 10 multiples for each of these numbers, 146 and 106:

First 10 Multiples of 146: 146, 292, 438, 584, 730, 876, 1022, 1168, 1314, 1460

First 10 Multiples of 106: 106, 212, 318, 424, 530, 636, 742, 848, 954, 1060

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 146 and 106 are 7738, 15476, 23214. Because 7738 is the smallest, it is the least common multiple.

The LCM of 146 and 106 is 7738.

Math Tutor Suggests: Find the LCM of Other Number Pairs

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

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