#include <bits/stdc++.h>
using namespace std;
int main(){
  int T;
  cin >> T;
  for (int i = 0; i < T; i++){
    long long A, B, K;
    cin >> A >> B >> K;
    long long L = lcm(A, B);
    long long tv = 0, fv = 6100000000000000000;
    while (fv - tv > 1){
      long long mid = tv + (fv - tv) / 2;
      long long cnt = mid - mid / A - mid / B + mid / L;
      if (cnt <= K){
        tv = mid;
      } else {
        fv = mid;
      }
    }
    cout << tv << endl;
  }
}