Q:

What is the LCM of 32 and 66?

Accepted Solution

A:
Solution: The LCM of 32 and 66 is 1056 Methods How to find the LCM of 32 and 66 using Prime Factorization One way to find the LCM of 32 and 66 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 32? What are the Factors of 66? Here is the prime factorization of 32: 2 5 2^5 2 5 And this 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 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 5 × 3 1 × 1 1 1 = 1056 2^5 × 3^1 × 11^1 = 1056 2 5 × 3 1 × 1 1 1 = 1056 Through this we see that the LCM of 32 and 66 is 1056. How to Find the LCM of 32 and 66 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 32 and 66 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, 32 and 66: What are the Multiples of 32? What are the Multiples of 66? Let’s take a look at the first 10 multiples for each of these numbers, 32 and 66: First 10 Multiples of 32: 32, 64, 96, 128, 160, 192, 224, 256, 288, 320 First 10 Multiples of 66: 66, 132, 198, 264, 330, 396, 462, 528, 594, 660 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 32 and 66 are 1056, 2112, 3168. Because 1056 is the smallest, it is the least common multiple. The LCM of 32 and 66 is 1056. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 106 and 85? What is the LCM of 102 and 75? What is the LCM of 70 and 114? What is the LCM of 105 and 40? What is the LCM of 132 and 13?