Q:

What is the LCM of 28 and 59?

Accepted Solution

A:
Solution: The LCM of 28 and 59 is 1652 Methods How to find the LCM of 28 and 59 using Prime Factorization One way to find the LCM of 28 and 59 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 28? What are the Factors of 59? Here is the prime factorization of 28: 2 2 × 7 1 2^2 × 7^1 2 2 × 7 1 And this is the prime factorization of 59: 5 9 1 59^1 5 9 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, 59 2 2 × 7 1 × 5 9 1 = 1652 2^2 × 7^1 × 59^1 = 1652 2 2 × 7 1 × 5 9 1 = 1652 Through this we see that the LCM of 28 and 59 is 1652. How to Find the LCM of 28 and 59 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 28 and 59 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, 28 and 59: What are the Multiples of 28? What are the Multiples of 59? Let’s take a look at the first 10 multiples for each of these numbers, 28 and 59: First 10 Multiples of 28: 28, 56, 84, 112, 140, 168, 196, 224, 252, 280 First 10 Multiples of 59: 59, 118, 177, 236, 295, 354, 413, 472, 531, 590 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 28 and 59 are 1652, 3304, 4956. Because 1652 is the smallest, it is the least common multiple. The LCM of 28 and 59 is 1652. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 50 and 3? What is the LCM of 6 and 9? What is the LCM of 2 and 40? What is the LCM of 112 and 132? What is the LCM of 111 and 129?