Q:

What is the LCM of 40 and 96?

Accepted Solution

A:
Solution: The LCM of 40 and 96 is 480 Methods How to find the LCM of 40 and 96 using Prime Factorization One way to find the LCM of 40 and 96 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 40? What are the Factors of 96? Here is the prime factorization of 40: 2 3 × 5 1 2^3 × 5^1 2 3 × 5 1 And this is the prime factorization of 96: 2 5 × 3 1 2^5 × 3^1 2 5 × 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, 5, 3 2 5 × 3 1 × 5 1 = 480 2^5 × 3^1 × 5^1 = 480 2 5 × 3 1 × 5 1 = 480 Through this we see that the LCM of 40 and 96 is 480. How to Find the LCM of 40 and 96 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 40 and 96 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, 40 and 96: What are the Multiples of 40? What are the Multiples of 96? Let’s take a look at the first 10 multiples for each of these numbers, 40 and 96: First 10 Multiples of 40: 40, 80, 120, 160, 200, 240, 280, 320, 360, 400 First 10 Multiples of 96: 96, 192, 288, 384, 480, 576, 672, 768, 864, 960 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 40 and 96 are 480, 960, 1440. Because 480 is the smallest, it is the least common multiple. The LCM of 40 and 96 is 480. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 137 and 81? What is the LCM of 128 and 71? What is the LCM of 98 and 66? What is the LCM of 70 and 52? What is the LCM of 86 and 27?