Problem 5

2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder.

What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?

Solution

// 2520 is the smallest number that can be

// divided by each of the numbers from 1 to 10

// without any remainder.

 

// What is the smallest positive number

// that is evenly divisible by all of the

// numbers from 1 to 20? 

 

namespace ProjectEulerCSharp_005

{

    class Program

    {

        static void Main(string[] args)

        {

            //have we found the answer yet?

            //let’s start off by saying "no"

            bool notFound = true;

            //20 seems like as good of a

            //starting spot as any

            long candidate = 20;

            while(notFound)

            {

                //I am incrementing up front

                //so that my loop exits elegantly

                candidate++;

 

                //here I am assuming that this candidate

                //is the answer.  I set it back when I

                //find a divisor that it doesn’t work for

                notFound = false;

 

                //this is not too important, but it’s a good

                //idea to start with the small numbers first because

                //they are more likely to fail

                for (int divisor = 2; divisor <= 20; divisor++)

                {

                    if (candidate % divisor != 0)

                    {

                        notFound = true;

                        break;

                    }

                }

            }

 

            System.Console.WriteLine(candidate);

        }

    }

}

Discussion

The brute force approach is pretty silly, but it does work and within the 1 minute rule.  It takes about 7.5 seconds on my 6 month old laptop.  When this problem was announced (November 2001) the same code would have probably taken over 10 minutes to complete – at least according to my back of the napkin estimation of Moore’s law.  🙂

If you have questions, leave a comment or please find me on Twitter (@azzlsoft) or email (rich@azzlsoft.com).