Q:

What is the LCM of 128 and 54?

Accepted Solution

A:
Solution: The LCM of 128 and 54 is 3456 Methods How to find the LCM of 128 and 54 using Prime Factorization One way to find the LCM of 128 and 54 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 54? Here is the prime factorization of 128: 2 7 2^7 2 7 And this is the prime factorization of 54: 2 1 × 3 3 2^1 × 3^3 2 1 × 3 3 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 2 7 × 3 3 = 3456 2^7 × 3^3 = 3456 2 7 × 3 3 = 3456 Through this we see that the LCM of 128 and 54 is 3456. How to Find the LCM of 128 and 54 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 128 and 54 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 54: What are the Multiples of 128? What are the Multiples of 54? Let’s take a look at the first 10 multiples for each of these numbers, 128 and 54: First 10 Multiples of 128: 128, 256, 384, 512, 640, 768, 896, 1024, 1152, 1280 First 10 Multiples of 54: 54, 108, 162, 216, 270, 324, 378, 432, 486, 540 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 54 are 3456, 6912, 10368. Because 3456 is the smallest, it is the least common multiple. The LCM of 128 and 54 is 3456. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 119 and 7? What is the LCM of 107 and 123? What is the LCM of 30 and 56? What is the LCM of 103 and 25? What is the LCM of 145 and 35?