Q:

What is the LCM of 14 and 32?

Accepted Solution

A:
Solution: The LCM of 14 and 32 is 224 Methods How to find the LCM of 14 and 32 using Prime Factorization One way to find the LCM of 14 and 32 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 14? What are the Factors of 32? Here is the prime factorization of 14: 2 1 × 7 1 2^1 × 7^1 2 1 × 7 1 And this is the prime factorization of 32: 2 5 2^5 2 5 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 5 × 7 1 = 224 2^5 × 7^1 = 224 2 5 × 7 1 = 224 Through this we see that the LCM of 14 and 32 is 224. How to Find the LCM of 14 and 32 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 14 and 32 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, 14 and 32: What are the Multiples of 14? What are the Multiples of 32? Let’s take a look at the first 10 multiples for each of these numbers, 14 and 32: First 10 Multiples of 14: 14, 28, 42, 56, 70, 84, 98, 112, 126, 140 First 10 Multiples of 32: 32, 64, 96, 128, 160, 192, 224, 256, 288, 320 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 14 and 32 are 224, 448, 672. Because 224 is the smallest, it is the least common multiple. The LCM of 14 and 32 is 224. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 96 and 122? What is the LCM of 143 and 146? What is the LCM of 78 and 57? What is the LCM of 7 and 52? What is the LCM of 1 and 3?