Q:

What is the LCM of 111 and 106?

Accepted Solution

A:
Solution: The LCM of 111 and 106 is 11766 Methods How to find the LCM of 111 and 106 using Prime Factorization One way to find the LCM of 111 and 106 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 111? What are the Factors of 106? Here is the prime factorization of 111: 3 1 × 3 7 1 3^1 × 37^1 3 1 × 3 7 1 And this is the prime factorization of 106: 2 1 × 5 3 1 2^1 × 53^1 2 1 × 5 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, 37, 2, 53 2 1 × 3 1 × 3 7 1 × 5 3 1 = 11766 2^1 × 3^1 × 37^1 × 53^1 = 11766 2 1 × 3 1 × 3 7 1 × 5 3 1 = 11766 Through this we see that the LCM of 111 and 106 is 11766. How to Find the LCM of 111 and 106 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 111 and 106 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, 111 and 106: What are the Multiples of 111? What are the Multiples of 106? Let’s take a look at the first 10 multiples for each of these numbers, 111 and 106: First 10 Multiples of 111: 111, 222, 333, 444, 555, 666, 777, 888, 999, 1110 First 10 Multiples of 106: 106, 212, 318, 424, 530, 636, 742, 848, 954, 1060 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 111 and 106 are 11766, 23532, 35298. Because 11766 is the smallest, it is the least common multiple. The LCM of 111 and 106 is 11766. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 149 and 93? What is the LCM of 14 and 128? What is the LCM of 127 and 36? What is the LCM of 76 and 40? What is the LCM of 2 and 35?