Q:

What is the LCM of 92 and 144?

Accepted Solution

A:
Solution: The LCM of 92 and 144 is 3312 Methods How to find the LCM of 92 and 144 using Prime Factorization One way to find the LCM of 92 and 144 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 92? What are the Factors of 144? Here is the prime factorization of 92: 2 2 × 2 3 1 2^2 × 23^1 2 2 × 2 3 1 And this is the prime factorization of 144: 2 4 × 3 2 2^4 × 3^2 2 4 × 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: 2, 23, 3 2 4 × 3 2 × 2 3 1 = 3312 2^4 × 3^2 × 23^1 = 3312 2 4 × 3 2 × 2 3 1 = 3312 Through this we see that the LCM of 92 and 144 is 3312. How to Find the LCM of 92 and 144 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 92 and 144 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, 92 and 144: What are the Multiples of 92? What are the Multiples of 144? Let’s take a look at the first 10 multiples for each of these numbers, 92 and 144: First 10 Multiples of 92: 92, 184, 276, 368, 460, 552, 644, 736, 828, 920 First 10 Multiples of 144: 144, 288, 432, 576, 720, 864, 1008, 1152, 1296, 1440 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 92 and 144 are 3312, 6624, 9936. Because 3312 is the smallest, it is the least common multiple. The LCM of 92 and 144 is 3312. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 9 and 76? What is the LCM of 33 and 130? What is the LCM of 13 and 43? What is the LCM of 86 and 63? What is the LCM of 16 and 103?