#include <bits/stdc++.h>
using namespace std;

void solve() {
	long long A, B, K;
	cin >> A >> B >> K;
	long long C = lcm(A, B), ok = 0, ng = 4500000000000000000LL, m;
	while( ok+1 < ng ) {
		m = (ok+ng)/2;
		if( m-(m/A+m/B-m/C) < K ) ok = m;
		else ng = m;
	}
	cout << ng << endl;
}

int main() {
	int T;
	cin >> T;
	while(T--) { solve(); }
}