/* -*- coding: utf-8 -*-
 *
 * 2526.cc:  No.2526 Kth Not-divisible Number - yukicoder
 */

#include<cstdio>
#include<algorithm>
 
using namespace std;

/* constant */

/* typedef */

typedef long long ll;

/* global variables */

/* subroutines */

template <typename T>
T gcd(T m, T n) {  // m >= 0, n >= 0
  if (m < n) swap(m, n);
  while (n > 0) {
    T r = m % n;
    m = n;
    n = r;
  }
  return m;
}

template <typename T>
T lcm(T m, T n) {
  return m * n / gcd<T>(m, n);
}

/* main */

int main() {
  int tn;
  scanf("%d", &tn);

  while (tn--) {
    int a, b;
    ll k;
    scanf("%d%d%lld", &a, &b, &k);

    ll l = lcm<ll>(a, b);
    ll r = l - l / a - l / b + 1;
    //printf("r=%lld\n", r);

    ll x0 = 0, x1 = 2000000000000000000LL;
    while (x0 + 1 < x1) {
      ll x = (x0 + x1) / 2;
      ll y = x % l;
      if (x / l * r + (y - y / a - y / b) >= k) x1 = x;
      else x0 = x;
    }

    printf("%lld\n", x1);
  }
  return 0;
}