#include <bits/stdc++.h>

using namespace std;

typedef long long ll;
typedef pair<int,int> P;
#define REP(i,n) for(int i=0;i<int(n);i++)



ll gcd(ll a,ll b){
	if(b==0) return a;
	else return gcd(b,a%b);
}


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

ll L;
void find(ll a,ll b,ll k){
     ll ng=0,ok=4e18;

     while(ok-ng>1){

          ll mid=(ng+ok)/2;

          if(k+mid/a+mid/b-mid/L<=mid) ok=mid;
          else ng=mid;

      }

     vector<ll> v;
     v.push_back(ok);
     if(ok>1) v.push_back(ok-1);
     if(ok>2) v.push_back(ok-2);
     if(ok>3) v.push_back(ok-3);

     for(int i=0;i<(int)v.size();i++) if(v[i]%a!=0 && v[i]%b!=0){
    	 cout << v[i] << endl;
    	 break;
     }

}

int main(void){
	cin.tie(nullptr);  ios_base::sync_with_stdio(false);
	int i,j;

	int T;
	cin >> T;
	while(T--){

		ll A,B,K;
		cin >> A >> B >> K;

		L=lcm(A,B);

		find(A,B,K);

	}



	return 0;
}