#include <bits/stdc++.h>
#include <atcoder/all>
using namespace std;
using namespace atcoder;
using ll = long long;
using ld = long double;
using mint = modint998244353;

ll lcm(ll a, ll b) {
  return a * b / gcd(a, b);
}

bool judge(ll x, ll a, ll b, ll c, ll k) {
  return (x - (x / a + x / b - x /c) >= k);
}

void solve() {
  ll A, B, K;
  cin >> A >> B >> K;
  ll C = lcm(A, B);
  ll l = 0, r = 4e18;
  while (r - l > 1) {
    ll x = (l + r) / 2;
    if (judge(x, A , B, C, K)) r = x;
    else l = x;
  }
  cout << r << endl;
}
int main() {
  int T; cin >> T;
  while (T--) {
    solve();
  }
  return 0;
}