My code

… was written in C++11 and can be compiled with G++, Clang++, Visual C++. You can download it, too. Or just jump to my GitHub repository.

The code contains #ifdefs to switch between the original problem and the Hackerrank version.
Enable #ifdef ORIGINAL to produce the result for the original problem (default setting for most problems).

       
#define ORIGINAL
       
 
       
#include <iostream>
       
 
       
// return minimum k where R(k) is divisible by x

       
unsigned long long getMinK(unsigned long long x)
       
{
       
  // same as gcd(x, 10) = 1
       
  if (x % 5 == 0 || x % 2 == 0)
       
    return 0;
       
 
       
  // "number of ones"
       
  unsigned long long result  = 1;
       
  // current repunit mod divisor
       
  unsigned long long repunit = 1;
       
  // no remainder ? that repunit can be divided by divisor
       
  while (repunit != 0)
       
  {
       
    // next repunit
       
    repunit *= 10;
       
    repunit++;
       
    // keep it mod divisor
       
    repunit %= x;
       
 
       
    result++;
       
  }
       
 
       
  return result;
       
}
       
 
       
int main()
       
{
       
  unsigned int tests;
       
  std::cin >> tests;
       
  while (tests--)
       
  {
       
    // I observed that getMinK(i) <= i
       
    // I lack the mathematic skills to prove (or disprove) it
       
    // at least it holds up to the result when running a brute-force search beginning at 1
       
    unsigned long long limit = 1000000;
       
    std::cin >> limit;
       
    unsigned long long i = limit;
       
 
       
#ifdef ORIGINAL
       
    while (getMinK(i) <= limit)
       
      i++;
       
    std::cout << i << std::endl;
       
#else
       
    std::cout << getMinK(i) << std::endl;
       
#endif
       
  }
       
  return 0;
       
}

This solution contains 7 empty lines, 10 comments and 5 preprocessor commands.