import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;

public class Main {
	public static void main(String[] args) throws Exception {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int t = Integer.parseInt(br.readLine());
		PrintWriter pw = new PrintWriter(System.out);
		for (int z = 0; z < t; z++) {
			String[] sa = br.readLine().split(" ");
			int a = Integer.parseInt(sa[0]);
			int b = Integer.parseInt(sa[1]);
			long k = Long.parseLong(sa[2]);

			long lcm = lcm(a, b);

			long ok = 4000000000000000000L;
			long ng = 0;
			while (Math.abs(ok - ng) > 1) {
				long mid = (ok + ng) / 2;
				long v1 = mid / a;
				long v2 = mid / b;
				long v3 = mid / lcm;
				long v4 = mid - v1 - v2 + v3;
				if (v4 >= k) {
					ok = mid;
				} else {
					ng = mid;
				}
			}
			pw.println(ok);
		}
		pw.flush();
		br.close();
	}

	static long lcm(long a, long b) {
		BigInteger ba = BigInteger.valueOf(a);
		BigInteger bb = BigInteger.valueOf(b);
		return ba.multiply(bb).divide(ba.gcd(bb)).longValue();
	}
}