#include <numeric>
#include <iostream>
#include <algorithm>
using namespace std;

// floor sum from: https://atcoder.jp/contests/practice2/submissions/16928474
long long floor_sum(long long n, long long m, long long a, long long b) {
	if (a >= m || b >= m) {
		return n * (n - 1) * (a / m) / 2 + n * (b / m) + floor_sum(n, m, a % m, b % m);
	}
	long long y = (n * a + b) / m, x = m * y - b;
	if (y == 0) {
		return 0;
	}
	return (n - (x + a - 1) / a) * y + floor_sum(y, a, m, (a - x % a) % a);
}

int main() {
	cin.tie(0);
	ios_base::sync_with_stdio(false);
	int T;
	cin >> T;
	for (int testcase = 1; testcase <= T; testcase++) {
		long long P, Q, K;
		cin >> P >> Q >> K;
		long long G = gcd(P, Q);
		P /= G;
		Q /= G;
		if (K >= (P - 1) * (Q - 1) / 2) {
			cout << (K + (P - 1) * (Q - 1) / 2) * G << '\n';
		}
		else {
			long long l = 0, r = P * Q;
			while (r - l > 1) {
				long long m = (l + r) / 2;
				// floor sum: floor(m / Q + 1) + floor((m - P) / Q + 1) + floor((m - 2 * P) / Q + 1) + ... + floor((m - k * P) / Q + 1) where k = floor(m / P)
				long long res = floor_sum(m / P + 1, Q, P, Q + m % P);
				if (res >= K + 1) {
					r = m;
				}
				else {
					l = m;
				}
			}
			cout << r * G << '\n';
		}
	}
	return 0;
}