Q:

What is the LCM of 144 and 43?

Accepted Solution

A:
Solution: The LCM of 144 and 43 is 6192 Methods How to find the LCM of 144 and 43 using Prime Factorization One way to find the LCM of 144 and 43 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 144? What are the Factors of 43? Here is the prime factorization of 144: 2 4 × 3 2 2^4 × 3^2 2 4 × 3 2 And this is the prime factorization of 43: 4 3 1 43^1 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, 43 2 4 × 3 2 × 4 3 1 = 6192 2^4 × 3^2 × 43^1 = 6192 2 4 × 3 2 × 4 3 1 = 6192 Through this we see that the LCM of 144 and 43 is 6192. How to Find the LCM of 144 and 43 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 144 and 43 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, 144 and 43: What are the Multiples of 144? What are the Multiples of 43? Let’s take a look at the first 10 multiples for each of these numbers, 144 and 43: First 10 Multiples of 144: 144, 288, 432, 576, 720, 864, 1008, 1152, 1296, 1440 First 10 Multiples of 43: 43, 86, 129, 172, 215, 258, 301, 344, 387, 430 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 144 and 43 are 6192, 12384, 18576. Because 6192 is the smallest, it is the least common multiple. The LCM of 144 and 43 is 6192. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 146 and 88? What is the LCM of 50 and 110? What is the LCM of 90 and 70? What is the LCM of 9 and 16? What is the LCM of 91 and 13?