#include <stdio.h>

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;
	else return (n - (x + a - 1) / a) * y + floor_sum(y, a, m, (a - x % a) % a);
}

long long solve(int P, int Q, int K)
{
	if (P == Q) return K;
	
	long long l = 1, r = (long long)P * K, m, n;
	while (l < r) {
		m = (l + r) / 2;
		n = m / P + 1;
		if (n > Q) n = Q;
		if (floor_sum(n, Q, P, m + Q - P * (n - 1)) <= K) l = m + 1;
		else r = m;
	}
	return l;
}

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

int main()
{
	int T, P, Q, K, G;
	scanf("%d", &T);
	while (T--) {
		scanf("%d %d %d", &P, &Q, &K);
		G = gcd(P, Q);
		P /= G;
		Q /= G;
		if (P > Q) {
			P ^= Q;
			Q ^= P;
			P ^= Q;
		}
		printf("%lld\n", solve(P, Q, K) * G);
	}
	fflush(stdout);
	return 0;
}