Q:

What is the LCM of 54 and 98?

Accepted Solution

A:
Solution: The LCM of 54 and 98 is 2646 Methods How to find the LCM of 54 and 98 using Prime Factorization One way to find the LCM of 54 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 54? What are the Factors of 98? Here is the prime factorization of 54: 2 1 × 3 3 2^1 × 3^3 2 1 × 3 3 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 1 × 3 3 × 7 2 = 2646 2^1 × 3^3 × 7^2 = 2646 2 1 × 3 3 × 7 2 = 2646 Through this we see that the LCM of 54 and 98 is 2646. How to Find the LCM of 54 and 98 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 54 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, 54 and 98: What are the Multiples of 54? What are the Multiples of 98? Let’s take a look at the first 10 multiples for each of these numbers, 54 and 98: First 10 Multiples of 54: 54, 108, 162, 216, 270, 324, 378, 432, 486, 540 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 54 and 98 are 2646, 5292, 7938. Because 2646 is the smallest, it is the least common multiple. The LCM of 54 and 98 is 2646. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 136 and 55? What is the LCM of 15 and 126? What is the LCM of 81 and 122? What is the LCM of 70 and 10? What is the LCM of 61 and 102?