Q:

What is the LCM of 54 and 93?

Accepted Solution

A:
Solution: The LCM of 54 and 93 is 1674 Methods How to find the LCM of 54 and 93 using Prime Factorization One way to find the LCM of 54 and 93 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 93? 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 93: 3 1 × 3 1 1 3^1 × 31^1 3 1 × 3 1 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, 31 2 1 × 3 3 × 3 1 1 = 1674 2^1 × 3^3 × 31^1 = 1674 2 1 × 3 3 × 3 1 1 = 1674 Through this we see that the LCM of 54 and 93 is 1674. How to Find the LCM of 54 and 93 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 54 and 93 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 93: What are the Multiples of 54? What are the Multiples of 93? Let’s take a look at the first 10 multiples for each of these numbers, 54 and 93: First 10 Multiples of 54: 54, 108, 162, 216, 270, 324, 378, 432, 486, 540 First 10 Multiples of 93: 93, 186, 279, 372, 465, 558, 651, 744, 837, 930 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 93 are 1674, 3348, 5022. Because 1674 is the smallest, it is the least common multiple. The LCM of 54 and 93 is 1674. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 84 and 66? What is the LCM of 126 and 16? What is the LCM of 144 and 137? What is the LCM of 95 and 122? What is the LCM of 133 and 140?