Q:

What is the LCM of 128 and 40?

Accepted Solution

A:
Solution: The LCM of 128 and 40 is 640 Methods How to find the LCM of 128 and 40 using Prime Factorization One way to find the LCM of 128 and 40 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 40? Here is the prime factorization of 128: 2 7 2^7 2 7 And this is the prime factorization of 40: 2 3 × 5 1 2^3 × 5^1 2 3 × 5 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, 5 2 7 × 5 1 = 640 2^7 × 5^1 = 640 2 7 × 5 1 = 640 Through this we see that the LCM of 128 and 40 is 640. How to Find the LCM of 128 and 40 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 128 and 40 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 40: What are the Multiples of 128? What are the Multiples of 40? Let’s take a look at the first 10 multiples for each of these numbers, 128 and 40: First 10 Multiples of 128: 128, 256, 384, 512, 640, 768, 896, 1024, 1152, 1280 First 10 Multiples of 40: 40, 80, 120, 160, 200, 240, 280, 320, 360, 400 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 40 are 640, 1280, 1920. Because 640 is the smallest, it is the least common multiple. The LCM of 128 and 40 is 640. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 113 and 140? What is the LCM of 28 and 94? What is the LCM of 51 and 117? What is the LCM of 120 and 111? What is the LCM of 123 and 29?