// gcd.cxx
/*****************************
/* This program will calculate the
/* greatest common devisor and
/* least common multiple of two integers.
/*
/* Written by: Lisa Venezia
/* Modified by: Amruth Kumar
/*****************************/

#include <iostream>
#include <cstdlib>

using std::cout;
using std::cin;
using std::endl;

int main()
{
   int num1;        // First number to be entered by the user
   int num2;        // Second number to be entered by the user
   int gcd;         // Greatest common divisor of the two integers
   int lcm;         // Least common multiple of the two integers

   // Robustly read the first positive integer
   cout << "Please enter the first positive integer: ";
   cin >> num1;
   while( num1 <= 0 )
   {
      cout << "Please re-enter a valid positive integer: ";
      cin >> num1;
   }

   // Robustly read the second positive integer
   cout << "Please enter the second positive integer: ";
   cin >> num2;
   while( num2 <= 0 )
   {
      cout << "Please re-enter a valid positive integer: ";
      cin >> num2;
   }

   // Set the smaller integer to be the tentative gcd
   if( num1 < num2 )        
   {
      gcd = num1;
   }
   else
   {
      gcd = num2;
   }

   // Test all the numbers from gcd down to 1 
   // until a number is found which evenly divides both the input integers
   while( gcd > 1 && !( (num1 % gcd  == 0) && (num2 % gcd == 0) ) )
   {
      gcd--;
   }

   // Report if the two numbers are relative primes
   if( 1 == gcd )
   {
      cout << num1 << " and " << num2 << " are relative primes\n";
   }

   // Find the least common multiple
   lcm = ( num1 * num2 ) / gcd;

   // Print the results
   cout << "The greatest common divisor of " << num1 << " and " << num2 
        << " is " << gcd << endl;
   cout << "The least common multiple of " << num1 << " and " << num2 
        << " is " << lcm << endl;;

   return EXIT_SUCCESS;
}