Q:

What is the LCM of 22 and 144?

Accepted Solution

A:
Solution: The LCM of 22 and 144 is 1584 Methods How to find the LCM of 22 and 144 using Prime Factorization One way to find the LCM of 22 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 22? What are the Factors of 144? Here is the prime factorization of 22: 2 1 × 1 1 1 2^1 × 11^1 2 1 × 1 1 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, 11, 3 2 4 × 3 2 × 1 1 1 = 1584 2^4 × 3^2 × 11^1 = 1584 2 4 × 3 2 × 1 1 1 = 1584 Through this we see that the LCM of 22 and 144 is 1584. How to Find the LCM of 22 and 144 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 22 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, 22 and 144: What are the Multiples of 22? What are the Multiples of 144? Let’s take a look at the first 10 multiples for each of these numbers, 22 and 144: First 10 Multiples of 22: 22, 44, 66, 88, 110, 132, 154, 176, 198, 220 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 22 and 144 are 1584, 3168, 4752. Because 1584 is the smallest, it is the least common multiple. The LCM of 22 and 144 is 1584. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 4 and 61? What is the LCM of 15 and 90? What is the LCM of 144 and 101? What is the LCM of 137 and 65? What is the LCM of 62 and 34?