Q:

What is the LCM of 96 and 133?

Accepted Solution

A:
Solution: The LCM of 96 and 133 is 12768 Methods How to find the LCM of 96 and 133 using Prime Factorization One way to find the LCM of 96 and 133 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 96? What are the Factors of 133? Here is the prime factorization of 96: 2 5 Γ— 3 1 2^5 Γ— 3^1 2 5 Γ— 3 1 And this is the prime factorization of 133: 7 1 Γ— 1 9 1 7^1 Γ— 19^1 7 1 Γ— 1 9 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, 3, 7, 19 2 5 Γ— 3 1 Γ— 7 1 Γ— 1 9 1 = 12768 2^5 Γ— 3^1 Γ— 7^1 Γ— 19^1 = 12768 2 5 Γ— 3 1 Γ— 7 1 Γ— 1 9 1 = 12768 Through this we see that the LCM of 96 and 133 is 12768. How to Find the LCM of 96 and 133 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 96 and 133 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, 96 and 133: What are the Multiples of 96? What are the Multiples of 133? Let’s take a look at the first 10 multiples for each of these numbers, 96 and 133: First 10 Multiples of 96: 96, 192, 288, 384, 480, 576, 672, 768, 864, 960 First 10 Multiples of 133: 133, 266, 399, 532, 665, 798, 931, 1064, 1197, 1330 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 96 and 133 are 12768, 25536, 38304. Because 12768 is the smallest, it is the least common multiple. The LCM of 96 and 133 is 12768. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 54 and 135? What is the LCM of 43 and 91? What is the LCM of 28 and 109? What is the LCM of 12 and 125? What is the LCM of 140 and 97?