Q:

What is the LCM of 58 and 80?

Accepted Solution

A:
Solution: The LCM of 58 and 80 is 2320 Methods How to find the LCM of 58 and 80 using Prime Factorization One way to find the LCM of 58 and 80 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 58? What are the Factors of 80? Here is the prime factorization of 58: 2 1 × 2 9 1 2^1 × 29^1 2 1 × 2 9 1 And this is the prime factorization of 80: 2 4 × 5 1 2^4 × 5^1 2 4 × 5 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, 29, 5 2 4 × 5 1 × 2 9 1 = 2320 2^4 × 5^1 × 29^1 = 2320 2 4 × 5 1 × 2 9 1 = 2320 Through this we see that the LCM of 58 and 80 is 2320. How to Find the LCM of 58 and 80 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 58 and 80 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, 58 and 80: What are the Multiples of 58? What are the Multiples of 80? Let’s take a look at the first 10 multiples for each of these numbers, 58 and 80: First 10 Multiples of 58: 58, 116, 174, 232, 290, 348, 406, 464, 522, 580 First 10 Multiples of 80: 80, 160, 240, 320, 400, 480, 560, 640, 720, 800 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 58 and 80 are 2320, 4640, 6960. Because 2320 is the smallest, it is the least common multiple. The LCM of 58 and 80 is 2320. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 30 and 8? What is the LCM of 136 and 110? What is the LCM of 49 and 94? What is the LCM of 129 and 112? What is the LCM of 6 and 137?