Q:

What is the LCM of 96 and 98?

Accepted Solution

A:
Solution: The LCM of 96 and 98 is 4704 Methods How to find the LCM of 96 and 98 using Prime Factorization One way to find the LCM of 96 and 98 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 98? Here is the prime factorization of 96: 2 5 × 3 1 2^5 × 3^1 2 5 × 3 1 And this is the prime factorization of 98: 2 1 × 7 2 2^1 × 7^2 2 1 × 7 2 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 2 5 × 3 1 × 7 2 = 4704 2^5 × 3^1 × 7^2 = 4704 2 5 × 3 1 × 7 2 = 4704 Through this we see that the LCM of 96 and 98 is 4704. How to Find the LCM of 96 and 98 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 96 and 98 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 98: What are the Multiples of 96? What are the Multiples of 98? Let’s take a look at the first 10 multiples for each of these numbers, 96 and 98: First 10 Multiples of 96: 96, 192, 288, 384, 480, 576, 672, 768, 864, 960 First 10 Multiples of 98: 98, 196, 294, 392, 490, 588, 686, 784, 882, 980 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 98 are 4704, 9408, 14112. Because 4704 is the smallest, it is the least common multiple. The LCM of 96 and 98 is 4704. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 144 and 142? What is the LCM of 34 and 26? What is the LCM of 33 and 125? What is the LCM of 132 and 84? What is the LCM of 46 and 53?