Q:

What is the LCM of 16 and 56?

Accepted Solution

A:
Solution: The LCM of 16 and 56 is 112 Methods How to find the LCM of 16 and 56 using Prime Factorization One way to find the LCM of 16 and 56 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 16? What are the Factors of 56? Here is the prime factorization of 16: 2 4 2^4 2 4 And this is the prime factorization of 56: 2 3 × 7 1 2^3 × 7^1 2 3 × 7 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: 2, 7 2 4 × 7 1 = 112 2^4 × 7^1 = 112 2 4 × 7 1 = 112 Through this we see that the LCM of 16 and 56 is 112. How to Find the LCM of 16 and 56 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 16 and 56 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, 16 and 56: What are the Multiples of 16? What are the Multiples of 56? Let’s take a look at the first 10 multiples for each of these numbers, 16 and 56: First 10 Multiples of 16: 16, 32, 48, 64, 80, 96, 112, 128, 144, 160 First 10 Multiples of 56: 56, 112, 168, 224, 280, 336, 392, 448, 504, 560 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 16 and 56 are 112, 224, 336. Because 112 is the smallest, it is the least common multiple. The LCM of 16 and 56 is 112. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 87 and 133? What is the LCM of 125 and 102? What is the LCM of 142 and 99? What is the LCM of 29 and 17? What is the LCM of 89 and 15?