Q:

What is the LCM of 90 and 48?

Accepted Solution

A:
Solution: The LCM of 90 and 48 is 720 Methods How to find the LCM of 90 and 48 using Prime Factorization One way to find the LCM of 90 and 48 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 90? What are the Factors of 48? Here is the prime factorization of 90: 2 1 × 3 2 × 5 1 2^1 × 3^2 × 5^1 2 1 × 3 2 × 5 1 And this is the prime factorization of 48: 2 4 × 3 1 2^4 × 3^1 2 4 × 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, 5 2 4 × 3 2 × 5 1 = 720 2^4 × 3^2 × 5^1 = 720 2 4 × 3 2 × 5 1 = 720 Through this we see that the LCM of 90 and 48 is 720. How to Find the LCM of 90 and 48 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 90 and 48 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, 90 and 48: What are the Multiples of 90? What are the Multiples of 48? Let’s take a look at the first 10 multiples for each of these numbers, 90 and 48: First 10 Multiples of 90: 90, 180, 270, 360, 450, 540, 630, 720, 810, 900 First 10 Multiples of 48: 48, 96, 144, 192, 240, 288, 336, 384, 432, 480 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 90 and 48 are 720, 1440, 2160. Because 720 is the smallest, it is the least common multiple. The LCM of 90 and 48 is 720. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 24 and 97? What is the LCM of 21 and 86? What is the LCM of 88 and 102? What is the LCM of 39 and 33? What is the LCM of 118 and 60?