Q:

What is the LCM of 48 and 83?

Accepted Solution

A:
Solution: The LCM of 48 and 83 is 3984 Methods How to find the LCM of 48 and 83 using Prime Factorization One way to find the LCM of 48 and 83 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 48? What are the Factors of 83? Here is the prime factorization of 48: 2 4 × 3 1 2^4 × 3^1 2 4 × 3 1 And this is the prime factorization of 83: 8 3 1 83^1 8 3 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, 83 2 4 × 3 1 × 8 3 1 = 3984 2^4 × 3^1 × 83^1 = 3984 2 4 × 3 1 × 8 3 1 = 3984 Through this we see that the LCM of 48 and 83 is 3984. How to Find the LCM of 48 and 83 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 48 and 83 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, 48 and 83: What are the Multiples of 48? What are the Multiples of 83? Let’s take a look at the first 10 multiples for each of these numbers, 48 and 83: First 10 Multiples of 48: 48, 96, 144, 192, 240, 288, 336, 384, 432, 480 First 10 Multiples of 83: 83, 166, 249, 332, 415, 498, 581, 664, 747, 830 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 48 and 83 are 3984, 7968, 11952. Because 3984 is the smallest, it is the least common multiple. The LCM of 48 and 83 is 3984. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 86 and 42? What is the LCM of 92 and 78? What is the LCM of 95 and 68? What is the LCM of 108 and 30? What is the LCM of 5 and 65?