Q:

What is the LCM of 33 and 113?

Accepted Solution

A:
Solution: The LCM of 33 and 113 is 3729 Methods How to find the LCM of 33 and 113 using Prime Factorization One way to find the LCM of 33 and 113 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 33? What are the Factors of 113? Here is the prime factorization of 33: 3 1 × 1 1 1 3^1 × 11^1 3 1 × 1 1 1 And this is the prime factorization of 113: 11 3 1 113^1 11 3 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: 3, 11, 113 3 1 × 1 1 1 × 11 3 1 = 3729 3^1 × 11^1 × 113^1 = 3729 3 1 × 1 1 1 × 11 3 1 = 3729 Through this we see that the LCM of 33 and 113 is 3729. How to Find the LCM of 33 and 113 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 33 and 113 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, 33 and 113: What are the Multiples of 33? What are the Multiples of 113? Let’s take a look at the first 10 multiples for each of these numbers, 33 and 113: First 10 Multiples of 33: 33, 66, 99, 132, 165, 198, 231, 264, 297, 330 First 10 Multiples of 113: 113, 226, 339, 452, 565, 678, 791, 904, 1017, 1130 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 33 and 113 are 3729, 7458, 11187. Because 3729 is the smallest, it is the least common multiple. The LCM of 33 and 113 is 3729. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 46 and 32? What is the LCM of 23 and 110? What is the LCM of 94 and 100? What is the LCM of 48 and 15? What is the LCM of 125 and 93?