#include <stdio.h>

long long gcd (long long a, long long b) {
  if (b <= 0LL) {
    return a;
  }
  
  return gcd(b, a%b);
}

int main () {
  int t = 0;
  long long a = 0LL;
  long long b = 0LL;
  long long k = 0LL;
  
  int res = 0;
  
  res = scanf("%d", &t);
  while (t > 0) {
    long long lcm = 0LL;
    long long ans[2] = { 0LL, 4000000000000000000LL };
    res = scanf("%lld", &a);
    res = scanf("%lld", &b);
    res = scanf("%lld", &k);
    lcm = (a*b)/gcd(a, b);
    while (ans[1]-ans[0] > 1LL) {
      long long cnt = 0LL;
      long long nxt = (ans[0] + ans[1]) / 2LL;
      cnt = nxt/a;
      cnt += nxt/b;
      cnt -= nxt/lcm;
      if (nxt-cnt < k) {
        ans[0] = nxt;
      } else {
        ans[1] = nxt;
      }
    }
    printf("%lld\n", ans[1]);
    t--;
  }
  
  return 0;
}