Q:

What is the LCM of 128 and 28?

Accepted Solution

A:
Solution: The LCM of 128 and 28 is 896 Methods How to find the LCM of 128 and 28 using Prime Factorization One way to find the LCM of 128 and 28 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 128? What are the Factors of 28? Here is the prime factorization of 128: 2 7 2^7 2 7 And this is the prime factorization of 28: 2 2 × 7 1 2^2 × 7^1 2 2 × 7 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 2 7 × 7 1 = 896 2^7 × 7^1 = 896 2 7 × 7 1 = 896 Through this we see that the LCM of 128 and 28 is 896. How to Find the LCM of 128 and 28 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 128 and 28 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, 128 and 28: What are the Multiples of 128? What are the Multiples of 28? Let’s take a look at the first 10 multiples for each of these numbers, 128 and 28: First 10 Multiples of 128: 128, 256, 384, 512, 640, 768, 896, 1024, 1152, 1280 First 10 Multiples of 28: 28, 56, 84, 112, 140, 168, 196, 224, 252, 280 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 128 and 28 are 896, 1792, 2688. Because 896 is the smallest, it is the least common multiple. The LCM of 128 and 28 is 896. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 25 and 82? What is the LCM of 84 and 47? What is the LCM of 43 and 30? What is the LCM of 97 and 94? What is the LCM of 56 and 134?