Q:

What is the LCM of 83 and 9?

Accepted Solution

A:
Solution: The LCM of 83 and 9 is 747 Methods How to find the LCM of 83 and 9 using Prime Factorization One way to find the LCM of 83 and 9 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 83? What are the Factors of 9? Here is the prime factorization of 83: 8 3 1 83^1 8 3 1 And this is the prime factorization of 9: 3 2 3^2 3 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: 83, 3 3 2 × 8 3 1 = 747 3^2 × 83^1 = 747 3 2 × 8 3 1 = 747 Through this we see that the LCM of 83 and 9 is 747. How to Find the LCM of 83 and 9 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 83 and 9 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, 83 and 9: What are the Multiples of 83? What are the Multiples of 9? Let’s take a look at the first 10 multiples for each of these numbers, 83 and 9: First 10 Multiples of 83: 83, 166, 249, 332, 415, 498, 581, 664, 747, 830 First 10 Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90 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 83 and 9 are 747, 1494, 2241. Because 747 is the smallest, it is the least common multiple. The LCM of 83 and 9 is 747. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 112 and 92? What is the LCM of 33 and 118? What is the LCM of 76 and 128? What is the LCM of 132 and 42? What is the LCM of 14 and 63?