Q:

What is the LCM of 109 and 32?

Accepted Solution

A:
Solution: The LCM of 109 and 32 is 3488 Methods How to find the LCM of 109 and 32 using Prime Factorization One way to find the LCM of 109 and 32 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 109? What are the Factors of 32? Here is the prime factorization of 109: 10 9 1 109^1 10 9 1 And this is the prime factorization of 32: 2 5 2^5 2 5 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: 109, 2 2 5 × 10 9 1 = 3488 2^5 × 109^1 = 3488 2 5 × 10 9 1 = 3488 Through this we see that the LCM of 109 and 32 is 3488. How to Find the LCM of 109 and 32 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 109 and 32 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, 109 and 32: What are the Multiples of 109? What are the Multiples of 32? Let’s take a look at the first 10 multiples for each of these numbers, 109 and 32: First 10 Multiples of 109: 109, 218, 327, 436, 545, 654, 763, 872, 981, 1090 First 10 Multiples of 32: 32, 64, 96, 128, 160, 192, 224, 256, 288, 320 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 109 and 32 are 3488, 6976, 10464. Because 3488 is the smallest, it is the least common multiple. The LCM of 109 and 32 is 3488. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 75 and 33? What is the LCM of 100 and 126? What is the LCM of 111 and 21? What is the LCM of 31 and 133? What is the LCM of 99 and 66?