#include<iostream>

using ll = unsigned long long;

int main(void){
	int t;
	std::cin>>t;
	while(t--){
		ll a, b, k;
		std::cin>>a>>b>>k;
		ll l = 0, r = 4e18 + 100;
		while(l + 1 < r){
			ll m = (l+r) / 2;
			ll cnt = m - m/ a - m / b + m / (a*b);
			if(cnt >=k){
				r = m;
			}
			else{
				l = m;
			}
		}
		std::cout << r << std::endl;
	}
}