Q:

What is the LCM of 101 and 55?

Accepted Solution

A:
Solution: The LCM of 101 and 55 is 5555 Methods How to find the LCM of 101 and 55 using Prime Factorization One way to find the LCM of 101 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 101? What are the Factors of 55? Here is the prime factorization of 101: 10 1 1 101^1 10 1 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: 101, 5, 11 5 1 × 1 1 1 × 10 1 1 = 5555 5^1 × 11^1 × 101^1 = 5555 5 1 × 1 1 1 × 10 1 1 = 5555 Through this we see that the LCM of 101 and 55 is 5555. How to Find the LCM of 101 and 55 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 101 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, 101 and 55: What are the Multiples of 101? What are the Multiples of 55? Let’s take a look at the first 10 multiples for each of these numbers, 101 and 55: First 10 Multiples of 101: 101, 202, 303, 404, 505, 606, 707, 808, 909, 1010 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 101 and 55 are 5555, 11110, 16665. Because 5555 is the smallest, it is the least common multiple. The LCM of 101 and 55 is 5555. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 27 and 76? What is the LCM of 11 and 87? What is the LCM of 122 and 73? What is the LCM of 106 and 22? What is the LCM of 42 and 44?