#include<bits/stdc++.h>
using namespace std;
using ll=long long;
using pii=pair<int,int>;

#define all(a) a.begin(),a.end()
#define pb push_back
#define sz(a) ((int)a.size())

const int maxn=1000005,mod=1000000007;
ll floor_sum(ll n, ll m, ll a, ll b) {
  ll ans = 0;
  if (a >= m) ans += (n - 1) * n * (a / m) / 2, a %= m;
  if (b >= m) ans += n * (b / m), b %= m;
  ll y_max = (a * n + b) / m, x_max = (y_max * m - b);
  if (y_max == 0) return ans;
  ans += (n - (x_max + a - 1) / a) * y_max;
  ans += floor_sum(y_max, a, m, (a - x_max % a) % a);
  return ans;
}

signed main(){
    ios_base::sync_with_stdio(0),cin.tie(0);
    int t; cin >> t;
    while(t--){
        int x,y,k; cin >> x >> y >> k;
        int g=__gcd(x,y); x/=g,y/=g;
        ll l=1,r=1e18;
        while(l<r){
            ll mid=l+r>>1;
            ll m=min(mid/x+1,(ll)y);
            if(floor_sum(m,y,x,mid-(m-1)*x)+m>=k+1) r=mid;
            else l=mid+1;
        }
        cout << l*g << "\n";
    }
}