Q:

What is the LCM of 107 and 55?

Accepted Solution

A:
Solution: The LCM of 107 and 55 is 5885 Methods How to find the LCM of 107 and 55 using Prime Factorization One way to find the LCM of 107 and 55 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 107? What are the Factors of 55? Here is the prime factorization of 107: 10 7 1 107^1 10 7 1 And this is the prime factorization of 55: 5 1 × 1 1 1 5^1 × 11^1 5 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: 107, 5, 11 5 1 × 1 1 1 × 10 7 1 = 5885 5^1 × 11^1 × 107^1 = 5885 5 1 × 1 1 1 × 10 7 1 = 5885 Through this we see that the LCM of 107 and 55 is 5885. How to Find the LCM of 107 and 55 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 107 and 55 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, 107 and 55: What are the Multiples of 107? What are the Multiples of 55? Let’s take a look at the first 10 multiples for each of these numbers, 107 and 55: First 10 Multiples of 107: 107, 214, 321, 428, 535, 642, 749, 856, 963, 1070 First 10 Multiples of 55: 55, 110, 165, 220, 275, 330, 385, 440, 495, 550 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 107 and 55 are 5885, 11770, 17655. Because 5885 is the smallest, it is the least common multiple. The LCM of 107 and 55 is 5885. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 123 and 20? What is the LCM of 80 and 61? What is the LCM of 136 and 87? What is the LCM of 110 and 141? What is the LCM of 105 and 76?