Q:

What is the LCM of 112 and 146?

Accepted Solution

A:
Solution: The LCM of 112 and 146 is 8176 Methods How to find the LCM of 112 and 146 using Prime Factorization One way to find the LCM of 112 and 146 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 112? What are the Factors of 146? Here is the prime factorization of 112: 2 4 × 7 1 2^4 × 7^1 2 4 × 7 1 And this is the prime factorization of 146: 2 1 × 7 3 1 2^1 × 73^1 2 1 × 7 3 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, 7, 73 2 4 × 7 1 × 7 3 1 = 8176 2^4 × 7^1 × 73^1 = 8176 2 4 × 7 1 × 7 3 1 = 8176 Through this we see that the LCM of 112 and 146 is 8176. How to Find the LCM of 112 and 146 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 112 and 146 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, 112 and 146: What are the Multiples of 112? What are the Multiples of 146? Let’s take a look at the first 10 multiples for each of these numbers, 112 and 146: First 10 Multiples of 112: 112, 224, 336, 448, 560, 672, 784, 896, 1008, 1120 First 10 Multiples of 146: 146, 292, 438, 584, 730, 876, 1022, 1168, 1314, 1460 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 112 and 146 are 8176, 16352, 24528. Because 8176 is the smallest, it is the least common multiple. The LCM of 112 and 146 is 8176. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 70 and 146? What is the LCM of 20 and 128? What is the LCM of 10 and 144? What is the LCM of 68 and 122? What is the LCM of 148 and 103?