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.

       
#include <iostream>
       
#include <vector>
       
 
       
std::vector<unsigned int> primes;
       
 
       
// return phi(x) if x/phi(x) <= minQuotient (else the result is undefined but > minQuotient)

       
unsigned long long phi(unsigned long long x)
       
{
       
  // totient function can be computed by finding all prime factors p
       
  // and subtracting them from x
       
  auto result  = x;
       
  auto reduced = x;
       
  for (auto p : primes)
       
  {
       
    // prime factors have to be p <= sqrt
       
    if (p*p > reduced)
       
      break;
       
 
       
    // not a prime factor ...
       
    if (reduced % p != 0)
       
      continue;
       
 
       
    // prime factors may occur multiple times, remove them all
       
    do
       
    {
       
      reduced /= p;
       
    } while (reduced % p == 0);
       
 
       
    // but subtract from result only once
       
    result -= result / p;
       
  }
       
 
       
  // we only checked prime factors <= sqrt(x)
       
  // there might exist one (!) prime factor > sqrt(x)
       
  // e.g. 3 is a prime factor of 6, and 3 > sqrt(6)
       
  if (reduced > 1)
       
    result -= result / reduced;
       
 
       
  return result;
       
}
       
 
       
// return true if a1/b1 < a2/b2

       
bool isLess(unsigned long long a1, unsigned long long b1, unsigned long long a2, unsigned long long b2)
       
{
       
  // a1/b1 < a2/b2 is the same as
       
  // a1*b2 < a2*b1 if all numbers are positive
       
  return a1*b2 < a2*b1;
       
}
       
 
       
int main()
       
{
       
  unsigned int numerator   = 15499;
       
  unsigned int denominator = 94744;
       
 
       
  unsigned long long current = 1;
       
  for (unsigned int i = 2; ; i++)
       
  {
       
    bool isPrime = true;
       
 
       
    // test against all prime numbers we have so far (in ascending order)
       
    for (auto p : primes)
       
    {
       
      // next prime is too large to be a divisor ?
       
      if (p*p > i)
       
        break;
       
 
       
      // divisible ? => not prime
       
      if (i % p == 0)
       
      {
       
        isPrime = false;
       
        break;
       
      }
       
    }
       
 
       
    if (!isPrime)
       
      continue;
       
 
       
    // yes, we have a prime number
       
    primes.push_back(i);
       
 
       
    // multiply prime numbers until the ratio becomes too small
       
    current *= i;
       
    if (isLess(phi(current), current - 1, numerator, denominator))
       
      break;
       
  }
       
 
       
  // undo last prime
       
  current /= primes.back();
       
 
       
  // simple iterative scan
       
  for (unsigned int i = 1; ; i++)
       
  {
       
    auto next = current * i;
       
 
       
    // below threshold ?
       
    if (isLess(phi(next), next - 1, numerator, denominator))
       
    {
       
      std::cout << next << std::endl;
       
      break;
       
    }
       
  }
       
 
       
  return 0;
       
}

This solution contains 19 empty lines, 21 comments and 2 preprocessor commands.