Q:

What is the LCM of 14 and 23?

Accepted Solution

A:
Solution: The LCM of 14 and 23 is 322 Methods How to find the LCM of 14 and 23 using Prime Factorization One way to find the LCM of 14 and 23 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 23? 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 23: 2 3 1 23^1 2 3 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, 23 2 1 × 7 1 × 2 3 1 = 322 2^1 × 7^1 × 23^1 = 322 2 1 × 7 1 × 2 3 1 = 322 Through this we see that the LCM of 14 and 23 is 322. How to Find the LCM of 14 and 23 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 14 and 23 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 23: What are the Multiples of 14? What are the Multiples of 23? Let’s take a look at the first 10 multiples for each of these numbers, 14 and 23: First 10 Multiples of 14: 14, 28, 42, 56, 70, 84, 98, 112, 126, 140 First 10 Multiples of 23: 23, 46, 69, 92, 115, 138, 161, 184, 207, 230 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 23 are 322, 644, 966. Because 322 is the smallest, it is the least common multiple. The LCM of 14 and 23 is 322. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 147 and 78? What is the LCM of 114 and 80? What is the LCM of 32 and 69? What is the LCM of 137 and 118? What is the LCM of 39 and 128?