#include <bits/stdc++.h>
//#include <atcoder/all>
using namespace std;
//using namespace atcoder;
//using mint = modint998244353;
//const int mod = 998244353;
//using mint = modint1000000007;
//const int mod = 1000000007;
//const int INF = 1e9;
const long long LINF = 1e18;
#define rep(i, n) for (int i = 0; i < (n); ++i)
#define rep2(i,l,r)for(int i=(l);i<(r);++i)
#define rrep(i, n) for (int i = (n-1); i >= 0; --i)
#define rrep2(i,l,r)for(int i=(r-1);i>=(l);--i)
#define all(x) (x).begin(),(x).end()
#define allR(x) (x).rbegin(),(x).rend()
#define P pair<int,int>
template<typename A, typename B> inline bool chmax(A & a, const B & b) { if (a < b) { a = b; return true; } return false; }
template<typename A, typename B> inline bool chmin(A & a, const B & b) { if (a > b) { a = b; return true; } return false; }

int main() {
	ios::sync_with_stdio(false);
	cin.tie(nullptr);
	int t; cin >> t;
	while (t--) {
		long long a, b, k; cin >> a >> b >> k;
		if (a > b)swap(a, b);
		long long g = gcd(a, b);
		long long l = lcm(a, b);
		long long ng = 0;
		long long ok = LINF * 2;
		while (1 < abs(ok - ng)) {
			long long mid = (ng + ok) / 2;
			auto check = [&]() {
				long long val = mid;
				val -= mid / a;
				if (a != g) {
					val -= mid / b;
					val += mid / l;
				}
				return val >= k;
			};
			if (check()) ok = mid;
			else ng = mid;
		}
		cout << ok << endl;
	}
	return 0;
}