#include <bits/stdc++.h>
#include <atcoder/math>
using namespace std;
const long long INF = 1000000000000000000;
int main(){
  int T;
  cin >> T;
  for (int i = 0; i < T; i++){
    long long P, Q, K;
    cin >> P >> Q >> K;
    long long g = gcd(P, Q);
    P /= g;
    Q /= g;
    long long tv = INF, fv = 0;
    while (tv - fv > 1){
      long long mid = (tv + fv) / 2;
      long long cnt = 0;
      long long N = min(P, mid / Q + 1);
      cnt = atcoder::floor_sum(N, P, -Q, mid + P);
      if (cnt >= K + 1){
        tv = mid;
      } else {
        fv = mid;
      }
    }
    cout << tv * g << endl;
  }
}