Q:

What is the LCM of 32 and 89?

Accepted Solution

A:
Solution: The LCM of 32 and 89 is 2848 Methods How to find the LCM of 32 and 89 using Prime Factorization One way to find the LCM of 32 and 89 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 89? Here is the prime factorization of 32: 2 5 2^5 2 5 And this is the prime factorization of 89: 8 9 1 89^1 8 9 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, 89 2 5 × 8 9 1 = 2848 2^5 × 89^1 = 2848 2 5 × 8 9 1 = 2848 Through this we see that the LCM of 32 and 89 is 2848. How to Find the LCM of 32 and 89 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 32 and 89 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 89: What are the Multiples of 32? What are the Multiples of 89? Let’s take a look at the first 10 multiples for each of these numbers, 32 and 89: First 10 Multiples of 32: 32, 64, 96, 128, 160, 192, 224, 256, 288, 320 First 10 Multiples of 89: 89, 178, 267, 356, 445, 534, 623, 712, 801, 890 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 89 are 2848, 5696, 8544. Because 2848 is the smallest, it is the least common multiple. The LCM of 32 and 89 is 2848. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 123 and 15? What is the LCM of 127 and 46? What is the LCM of 42 and 59? What is the LCM of 57 and 144? What is the LCM of 62 and 4?