#include <bits/stdc++.h>
#include <atcoder/all>

typedef long long int ll;
typedef long double ld;

using namespace std;
using namespace atcoder;

#define inf 1010000000
#define llinf 1001000000000000000ll
#define pi 3.141592653589793238
#define rep(i, n) for(ll i = 0; i < (n); i++)
#define rep1(i, n) for(ll i = 1; i <= (n); i++)
#define rep2(i,l,r) for(ll i = (l); i < (r); i++)
#define per(i, n) for(ll i = (n)-1; i >= 0; i--)
#define each(x, v) for (auto&& x : v)
#define rng(a) a.begin(),a.end()
#define fi first
#define se second
#define pb push_back
#define eb emplace_back
#define pob pop_back
#define st string
#define sz(x) (int)(x).size()
#define mems(x) memset(x, -1, sizeof(x));
#define pcnt __builtin_popcountll
#define _GLIBCXX_DEBUG

#define dame { puts("-1"); return 0;}
#define yes { puts("Yes"); return 0;}
#define no { puts("No"); return 0;}
#define ret(x) { cout<<(x)<<endl;}
#define rets(x) { cout<<(x)<< " ";}
#define Endl cout<<endl;

template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return true; } return false;}
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return true; } return false;}

// 仮マクロ 便利だったら昇格
#define dump(x) { cout << #x << " = " << (x) << endl;}
#define bit(n) (1LL<<(n))
#define UNIQUE(v) v.erase( unique(v.begin(), v.end()), v.end())

template <class T = ll>
inline T in(){ T x; cin >> x; return (x);}

#define vcin(x,n) {for(ll loop=0; loop<(n); loop++) cin>>x[loop];}

// ここまで仮マクロ

// srand((unsigned)time(NULL)); rand()を用いる際にmainの頭に置く
// clock()/CLOCKS_PER_SEC 秒数を知りたいときに用いる

#define mod 998244353
using mint = modint998244353;

/*

#define mod 1000000007
using mint = modint1000000007;

*/

vector<ll> dx={1,0,-1,0};
vector<ll> dy={0,1,0,-1};

using pl = pair<ll,ll>;
using ppl = pair<ll,pl>;
using V = vector<ll>;
using Graph = vector<vector<ll>>;
// G.assign(n, vector<ll>()); グローバル変数にGを置く時に置く

// 関数を置くのはここ以下

ll frobenius(ll p, ll q, ll k) {
  ll ans = 0;
  ans -= floor_sum(k/q,p,q,q);
  ans += (k/q+1)*(k/p+1);
  ans--;
  ans += floor_sum(k/q,p,q,q);
  ans -= floor_sum(k/q,p,q,q+p-k%p-1);
  return ans;
}

// フロベニウスの硬貨交換問題を解く
// x,yのみの和で表せるk以下の数は何個あるか？(x,yは互いに素、kはx*y未満)


bool isOK(ll mid,ll p,ll q, ll k){
  ll ans = 0;
  ll tmp = gcd(p,q);
  mid /= tmp;
  p /= tmp;
  q /= tmp;
  if(mid>=p*q){
    ans += mid-p*q+1;
    mid = p*q-1;
  }
  if(k<=frobenius(p,q,mid)) return true;
  return false;
}

ll b_se(ll p,ll q,ll k) {
  ll ng = 0;
  ll ok = p*k; //okは必ずtrue, ngは必ずfalse

  while (abs(ok - ng) > 1) {
    ll mid = (ok + ng) / 2;

    if (isOK(mid,p,q,k)) ok = mid;
    else ng = mid;
  }
  return ok;
}

int main() {
  cin.tie(nullptr);
  ios::sync_with_stdio(false);
  cout << fixed << setprecision(20);
  ll t = in();
  rep(_,t){
    ll p,q,k; cin >> p >> q >> k;
    if(p>q) swap(p,q);
    ret(b_se(p,q,k))
  }

  rep(i,20){
    isOK(i+1,3,4,-1);
  }
}