Q:

What is the LCM of 12 and 22?

Accepted Solution

A:
Solution: The LCM of 12 and 22 is 132 Methods How to find the LCM of 12 and 22 using Prime Factorization One way to find the LCM of 12 and 22 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 12? What are the Factors of 22? Here is the prime factorization of 12: 2 2 × 3 1 2^2 × 3^1 2 2 × 3 1 And this is the prime factorization of 22: 2 1 × 1 1 1 2^1 × 11^1 2 1 × 1 1 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, 11 2 2 × 3 1 × 1 1 1 = 132 2^2 × 3^1 × 11^1 = 132 2 2 × 3 1 × 1 1 1 = 132 Through this we see that the LCM of 12 and 22 is 132. How to Find the LCM of 12 and 22 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 12 and 22 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, 12 and 22: What are the Multiples of 12? What are the Multiples of 22? Let’s take a look at the first 10 multiples for each of these numbers, 12 and 22: First 10 Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120 First 10 Multiples of 22: 22, 44, 66, 88, 110, 132, 154, 176, 198, 220 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 12 and 22 are 132, 264, 396. Because 132 is the smallest, it is the least common multiple. The LCM of 12 and 22 is 132. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 5 and 77? What is the LCM of 125 and 121? What is the LCM of 75 and 132? What is the LCM of 108 and 31? What is the LCM of 103 and 7?