Q:

What is the LCM of 125 and 40?

Accepted Solution

A:
Solution: The LCM of 125 and 40 is 1000 Methods How to find the LCM of 125 and 40 using Prime Factorization One way to find the LCM of 125 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 125? What are the Factors of 40? Here is the prime factorization of 125: 5 3 5^3 5 3 And this is the prime factorization of 40: 2 3 Γ— 5 1 2^3 Γ— 5^1 2 3 Γ— 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: 5, 2 2 3 Γ— 5 3 = 1000 2^3 Γ— 5^3 = 1000 2 3 Γ— 5 3 = 1000 Through this we see that the LCM of 125 and 40 is 1000. How to Find the LCM of 125 and 40 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 125 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, 125 and 40: What are the Multiples of 125? What are the Multiples of 40? Let’s take a look at the first 10 multiples for each of these numbers, 125 and 40: First 10 Multiples of 125: 125, 250, 375, 500, 625, 750, 875, 1000, 1125, 1250 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 125 and 40 are 1000, 2000, 3000. Because 1000 is the smallest, it is the least common multiple. The LCM of 125 and 40 is 1000. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 19 and 3? What is the LCM of 39 and 128? What is the LCM of 71 and 86? What is the LCM of 10 and 113? What is the LCM of 134 and 56?