import java.io.*;
import java.util.*;
import java.util.stream.*;

public class Main {
    public static void main(String[] args) throws Exception {
        Scanner sc = new Scanner();
        int t = sc.nextInt();
        StringBuilder sb = new StringBuilder();
        while(t-- > 0) {
            int a = sc.nextInt();
            int b = sc.nextInt();
            long k = sc.nextLong();
            long lcm = getLCM(a, b);
            long left = 0;
            long right = Long.MAX_VALUE / 2;
            while (right - left > 1) {
                long m = (left + right) / 2;
                if (m - m / a - m / b + m / lcm <= k) {
                    left = m;
                } else {
                    right = m;
                }
            }
            sb.append(left).append("\n");
        }
        System.out.print(sb);
    }
    
    static long getLCM(long x, long y) {
        return x / getGCD(x, y) * y;
    }
    
    static long getGCD(long x, long y) {
        if (y == 0) {
            return x;
        } else {
            return getGCD(y, x % y);
        }
    }
} 
class Utilities {
    static String arrayToLineString(Object[] arr) {
        return Arrays.stream(arr).map(x -> x.toString()).collect(Collectors.joining("\n"));
    }
    
    static String arrayToLineString(int[] arr) {
        return String.join("\n", Arrays.stream(arr).mapToObj(String::valueOf).toArray(String[]::new));
    }
}
class Scanner {
    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    StringTokenizer st = new StringTokenizer("");
    StringBuilder sb = new StringBuilder();
    
    public Scanner() throws Exception {
        
    }
    
    public int nextInt() throws Exception {
        return Integer.parseInt(next());
    }
    
    public long nextLong() throws Exception {
        return Long.parseLong(next());
    }
    
    public double nextDouble() throws Exception {
        return Double.parseDouble(next());
    }
    
    public int[] nextIntArray() throws Exception {
        return Stream.of(br.readLine().split(" ")).mapToInt(Integer::parseInt).toArray();
    }
    
    public String next() throws Exception {
        while (!st.hasMoreTokens()) {
            st = new StringTokenizer(br.readLine());
        }
        return st.nextToken();
    }
    
}