Q:

What is the LCM of 47 and 110?

Accepted Solution

A:
Solution: The LCM of 47 and 110 is 5170 Methods How to find the LCM of 47 and 110 using Prime Factorization One way to find the LCM of 47 and 110 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 47? What are the Factors of 110? Here is the prime factorization of 47: 4 7 1 47^1 4 7 1 And this is the prime factorization of 110: 2 1 × 5 1 × 1 1 1 2^1 × 5^1 × 11^1 2 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: 47, 2, 5, 11 2 1 × 5 1 × 1 1 1 × 4 7 1 = 5170 2^1 × 5^1 × 11^1 × 47^1 = 5170 2 1 × 5 1 × 1 1 1 × 4 7 1 = 5170 Through this we see that the LCM of 47 and 110 is 5170. How to Find the LCM of 47 and 110 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 47 and 110 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, 47 and 110: What are the Multiples of 47? What are the Multiples of 110? Let’s take a look at the first 10 multiples for each of these numbers, 47 and 110: First 10 Multiples of 47: 47, 94, 141, 188, 235, 282, 329, 376, 423, 470 First 10 Multiples of 110: 110, 220, 330, 440, 550, 660, 770, 880, 990, 1100 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 47 and 110 are 5170, 10340, 15510. Because 5170 is the smallest, it is the least common multiple. The LCM of 47 and 110 is 5170. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 124 and 106? What is the LCM of 46 and 95? What is the LCM of 139 and 129? What is the LCM of 89 and 19? What is the LCM of 5 and 119?