Q:

What is the LCM of 66 and 33?

Accepted Solution

A:
Solution: The LCM of 66 and 33 is 66 Methods How to find the LCM of 66 and 33 using Prime Factorization One way to find the LCM of 66 and 33 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 66? What are the Factors of 33? Here is the prime factorization of 66: 2 1 × 3 1 × 1 1 1 2^1 × 3^1 × 11^1 2 1 × 3 1 × 1 1 1 And this is the prime factorization of 33: 3 1 × 1 1 1 3^1 × 11^1 3 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 1 × 3 1 × 1 1 1 = 66 2^1 × 3^1 × 11^1 = 66 2 1 × 3 1 × 1 1 1 = 66 Through this we see that the LCM of 66 and 33 is 66. How to Find the LCM of 66 and 33 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 66 and 33 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, 66 and 33: What are the Multiples of 66? What are the Multiples of 33? Let’s take a look at the first 10 multiples for each of these numbers, 66 and 33: First 10 Multiples of 66: 66, 132, 198, 264, 330, 396, 462, 528, 594, 660 First 10 Multiples of 33: 33, 66, 99, 132, 165, 198, 231, 264, 297, 330 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 66 and 33 are 66, 132, 198. Because 66 is the smallest, it is the least common multiple. The LCM of 66 and 33 is 66. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 65 and 84? What is the LCM of 142 and 106? What is the LCM of 27 and 88? What is the LCM of 103 and 76? What is the LCM of 39 and 140?