#include<bits/stdc++.h>
namespace {
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wunused-function"
#include<atcoder/all>
#pragma GCC diagnostic pop
using namespace std;
using namespace atcoder;
#define rep(i,n) for(int i = 0; i < (int)(n); i++)
#define rrep(i,n) for(int i = (int)(n) - 1; i >= 0; i--)
#define all(x) begin(x), end(x)
#define rall(x) rbegin(x), rend(x)
template<class T> bool chmax(T& a, const T& b) { if (a < b) { a = b; return true; } else return false; }
template<class T> bool chmin(T& a, const T& b) { if (b < a) { a = b; return true; } else return false; }
using ll = long long;
using P = pair<int,int>;
using VI = vector<int>;
using VVI = vector<VI>;
using VL = vector<ll>;
using VVL = vector<VL>;

} int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int tt;
  cin >> tt;
  while(tt--) {
    ll p, q, k;
    cin >> p >> q >> k;
    k++;
    ll g = gcd(p, q);
    ll l = p * q / g;
    ll q1 = q / g;
    ll cnt0 = floor_sum(q1, q, -p, l + q - 1);
    if (k > cnt0) {
      k -= cnt0;
      ll ans = l + (k - 1) * g;
      cout << ans << '\n';
      continue;
    }
    ll lb = 0, ub = l;
    while(ub - lb > 1) {
      ll c = (lb + ub) / 2;
      ll cnt = floor_sum((c + p - 1) / p, q, -p, c + q - 1);
      if (cnt >= k) ub = c;
      else lb = c;
    }
    cout << lb << '\n';
  }
}