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

ll MAX = 4e18;

int t;
ll a, b, k, g;

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

ll lcm(ll a, ll b) {
	return a * b / gcd(a, b);
}

ll f(ll x) {
	return x - (x / a) - (x / b) + (x / g);
}

ll calc(ll left, ll right) {
	ll mid = (left + right) / 2;

	ll cal = f(mid);
	if (cal == k) {
		ll x = mid;
		x = mid;
		while (f(x) == k) {
			if (x % a != 0 && x % b != 0) {
				return x;
			}
			x--;
		}
	}
	else if (cal > k) {
		return calc(left, mid);
	}
	else if (cal < k) {
		return calc(mid + 1, right);
	}
}


int main(void) {
	cin >> t;

	vector<ll> ans;
	while (t > 0) {
		cin >> a >> b >> k;
		g = lcm(a, b);

		ll res = calc(1, MAX);
		ans.push_back(res);

		t--;
	}

	for (int i = 0; i < ans.size(); i++) {
		cout << ans[i] << endl;
	}

	return 0;
}