#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
using namespace std;
#define FOR(i,m,n) for(int i=(m);i<(n);++i)
#define REP(i,n) FOR(i,0,n)
#define ALL(v) (v).begin(),(v).end()
using ll = long long;
constexpr int INF = 0x3f3f3f3f;
constexpr long long LINF = 0x3f3f3f3f3f3f3f3fLL;
constexpr double EPS = 1e-8;
constexpr int MOD = 998244353;
// constexpr int MOD = 1000000007;
constexpr int DY4[]{1, 0, -1, 0}, DX4[]{0, -1, 0, 1};
constexpr int DY8[]{1, 1, 0, -1, -1, -1, 0, 1};
constexpr int DX8[]{0, -1, -1, -1, 0, 1, 1, 1};
template <typename T, typename U>
inline bool chmax(T& a, U b) { return a < b ? (a = b, true) : false; }
template <typename T, typename U>
inline bool chmin(T& a, U b) { return a > b ? (a = b, true) : false; }
struct IOSetup {
  IOSetup() {
    std::cin.tie(nullptr);
    std::ios_base::sync_with_stdio(false);
    std::cout << fixed << setprecision(20);
  }
} iosetup;

long long floor_sum(long long a, long long b, long long m, long long n) {
  long long res = 0;
  if (a < 0) {
    long long nxt_a = a % m;
    if (nxt_a < 0) nxt_a += m;
    res -= n * (n - 1) / 2 * ((nxt_a - a) / m);
    a = nxt_a;
  }
  if (b < 0) {
    long long nxt_b = b % m;
    if (nxt_b < 0) nxt_b += m;
    res -= n * ((nxt_b - b) / m);
    b = nxt_b;
  }
  while (true) {
    if (a >= m) {
      res += n * (n - 1) / 2 * (a / m);
      a %= m;
    }
    if (b >= m) {
      res += n * (b / m);
      b %= m;
    }
    const long long y_max = a * n + b;
    if (y_max < m) break;
    b = y_max % m;
    n = y_max / m;
    std::swap(a, m);
  }
  return res;
}

void solve() {
  int p, q, k; cin >> p >> q >> k;
  const int g = gcd(p, q);
  p /= g; q /= g;
  if (p > q) swap(p, q);
  const ll less_than_pq = floor_sum(-p, 1LL * p * q - 1, q, q) + q - 1;
  if (less_than_pq < k) {
    cout << (1LL * p * q + (k - less_than_pq - 1)) * g << '\n';
    return;
  }
  ll lb = p - 1, ub = 1LL * p * q - 1;
  while (ub - lb > 1) {
    const ll mid = (lb + ub) / 2;
    (floor_sum(-p, mid, q, mid / p + 1) + mid / p < k ? lb : ub) = mid;
  }
  cout << ub * g << '\n';
}

int main() {
  int t; cin >> t;
  while (t--) solve();
  return 0;

  // FOR(p, 1, 100) FOR(q, 1, 100) {
  //   if (gcd(p, q) > 1) continue;
  //   set<int> s;
  //   REP(x, q) REP(y, p) {
  //     if (p * x + q * y < p * q) assert(s.emplace(p * x + q * y).second);
  //   }
  // }
}