import java.util.*; 
import java.io.*;
import java.math.*;
import java.util.stream.*;
import java.util.function.*;
import java.security.SecureRandom;

class Main implements Runnable
{   
    // 二分探索で、ある値(X)における.a,b,LCM(a,b)で割り切れる数(Y) -> X - Y == Kになる値を求めれば良いのかな?
    // あれ、lcmってO(logN)だっけ.そうだと信じる.
    void solve()
    {           
        int T = in.nextInt();
        while(T-->0)
        {
            long A = in.nextLong() , B = in.nextLong() , K = in.nextLong();
            long lcm = LCM(A , B);
            long l = 0 , r = (long) 1e19;
            while(r - l > 1)
            {
                long X = (r + l) / 2 ;
                long Kth = X - (((X / A) + (X / B)) - (X / lcm));
                if(Kth < K) l = X ;
                if(Kth >= K) r = X ;
            }
            out.println(r);
        }
    }

    public static void main(String ... args) 
    {
        new Thread(null, new Main(), "", Runtime.getRuntime().maxMemory()).start(); 
    }

    public void run() 
    {   
        solve();
        out.flush();
    }
    //ペア
    record IP(int fi , int se) { public String toString() { return fi +" "+ se ;} }
    record LP(long fi , long se) { public String toString() { return fi +" "+ se ;} }
    record SP(String fi , String se) { public String toString() { return fi +" "+se; } }
    //距離
    double MAN(LP p1 , LP p2) { return Math.abs(p1.fi - p2.fi) + Math.abs(p1.se - p2.se) ; }
    double EUC(LP p1 , LP p2) { return Math.sqrt((p1.fi - p2.fi) * (p1.fi - p2.fi) + (p1.se - p2.se) * (p1.se - p2.se)); }
    //階乗
    long REC(long a) { return a == 1 ? 1 : a * REC(a - 1); }
    //合計
    int  SUM(int ... a)  { int sum = 0 ; for(int p : a) sum += p ; return sum ;}
    long SUM(long ... a) { long sum = 0 ; for(long p : a) sum += p ; return sum ;}
    //最大
    int  MAX(int ... a) { int max = -1 ; for(int p : a) max = Math.max(max , p); return max; }
    long MAX(long ... a) { long max = -1 ; for(long p : a) max = Math.max(max , p); return max; }
    //最小
    int  MIN(int ... a) { int min = Integer.MAX_VALUE ; for(int p : a) min = Math.min(min , p); return min; }
    long MIN(long ... a) { long min = Long.MAX_VALUE ; for(long p : a) min = Math.min(min , p); return min; }
    //冪乗
    int  POW(int a  , int b) { return (int) Math.pow(a , b) ; }
    long POW(long a , long b) { return (long) Math.pow(a , b) ; }
    //最小公倍数
    int  LCM(int a, int b) { return a / GCD(a, b) * b; }
    long LCM(long a, long b) { return a / GCD(a, b) * b; }
    int  LCM(int ... a) { int lcm = 1 ; for(int p : a) lcm = LCM(lcm , p) ; return lcm ; }
    long LCM(long ... a) { long lcm = 1 ; for(long p : a) lcm = LCM(lcm , p) ; return lcm ; }
    BigInteger LCM(BigInteger x, BigInteger y) { return x.multiply(y).divide(Objects.nonNull(GCD(x, y)) ? GCD(x, y) : BigInteger.ONE); }
    BigInteger LCM(BigInteger ... arr) { return Stream.of(arr).reduce((x, y) -> LCM(x, y)).orElse(BigInteger.ONE); }
    //最大公約数
    int  GCD(int a, int b) { return b == 0 ? a: GCD(b, a % b); }
    long GCD(long a, long b) { return b == 0 ? a: GCD(b, a % b); }
    int  GCD(int ... a) { int gcd = 0 ; for(int p : a) gcd = GCD(gcd , p) ; return gcd ; }
    long GCD(long ... a) { long gcd = 0L ; for(long p : a) gcd = GCD(gcd , p) ; return gcd ; }
    BigInteger GCD(BigInteger x, BigInteger y) { return (Objects.nonNull(x) ? x : BigInteger.ONE).gcd(y); }
    BigInteger GCD(BigInteger ... arr) { return Stream.of(arr).reduce(BigInteger::gcd).orElse(BigInteger.ZERO); }
    //反転
    String  REVERSE(String a) { return new StringBuilder(a).reverse().toString(); }
    int  [] REVERSE(int [] a) { int [] r = new int[a.length] ; int idx = a.length ; for(int p : a) r[--idx] = p ; return r ; }
    long [] REVERSE(long [] a) { long [] r = new long[a.length] ; int idx = a.length ; for(long p : a) r[--idx] = p ; return r ; }
    //配列
    void FILL(int  [] a , int v) { Arrays.fill(a , v); }
    void FILL(long [] a , long v) { Arrays.fill(a , v); }
    void FILL(char [] a , char v) { Arrays.fill(a , v); }
    void FILL(int  [][] a , int v) { for(int [] aa : a) FILL(aa , v) ; }
    void FILL(long [][] a , long v) { for(long [] aa : a) FILL(aa , v) ; }
    void FILL(char [][] a , char v) { for(char [] aa : a) FILL(aa , v) ; }
    void FILL(int  [][][] a , int v) { for(int [][] aa : a) FILL(aa , v); }
    void FILL(long [][][] a , long v) { for(long [][] aa : a) FILL(aa , v); }
    int  [] COPY(int  [] a) { return Arrays.copyOf(a , a.length); } 
    long [] COPY(long [] a) { return Arrays.copyOf(a , a.length); } 
    char [] COPY(char [] a) { return Arrays.copyOf(a , a.length); } 
    //スワップ
    String SWAP(String s , int l , int r) { StringBuilder m = new StringBuilder(s) ;m.setCharAt(l, s.charAt(r)); m.setCharAt(r, s.charAt(l)); return m.toString(); }
    int [] SWAP(int [] a , int l , int r) { int tmp = a[l] ; a[l] = a[r] ; a[r] = tmp ; return a ; }
    long [] SWAP(long [] a , int l , int r) { long tmp = a[l] ; a[l] = a[r] ; a[r] = tmp ; return a ; }
    //ペア配列入力
    IP [] IPA(int n) { IP [] a = new IP[n]; for(int i = 0 ; i < n ; i ++ ) a[i] = new IP(in.nextInt() , in.nextInt()); return a ; }
    LP [] LPA(int n) { LP [] a = new LP[n]; for(int i = 0 ; i < n ; i ++ ) a[i] = new LP(in.nextLong() , in.nextLong()); return a ; }
    //進数
    String BIN(long a , int len) { String b = Long.toBinaryString(a); while(b.length() < len) b = "0" + b ; return b ; }
    //デバッグ
    void DEBUG(int [] a)  { out.println(Arrays.toString(a)); fl();}
    void DEBUG(long [] a) {  out.println(Arrays.toString(a)); fl();}
    void DEBUG(double [] a) { out.println(Arrays.toString(a)); fl();}
    void DEBUG(String [] a) { out.println(Arrays.toString(a)); fl();}
    void DEBUG(char [] a) { out.println(Arrays.toString(a)); fl();}
    void DEBUG(boolean [] a) { char [] c = CV(a); DEBUG(c); fl();}
    void DEBUG(int [][] a) { for(int i = 0 ; i < a.length ; i ++ ) out.println(Arrays.toString(a[i])); fl();}
    void DEBUG(long [][] a) { for(int i = 0 ; i < a.length ; i ++ ) out.println(Arrays.toString(a[i])); fl();}
    void DEBUG(double [][] a) { for(int i = 0 ; i < a.length ; i ++ ) out.println(Arrays.toString(a[i])); fl();}
    void DEBUG(String [][] a) { for(int i = 0 ; i < a.length ; i ++ ) out.println(Arrays.toString(a[i])); fl();}
    void DEBUG(char [][] a) { for(int i = 0 ; i < a.length ; i ++ ) out.println(Arrays.toString(a[i])); fl();}
    void DEBUG(boolean [][] a) { char [][] c = new char [a.length][a[0].length] ; for(int i = 0 ; i < a.length ; i ++ ) c[i] = CV(a[i]) ; DEBUG(c); fl();}
    private char [] CV(boolean [] a) { char [] c = new char[a.length] ; for(int i = 0 ; i < a.length ; i ++ ) c[i] = a[i] ? 'O' : 'X' ; return c ; }
    private void fl() { out.flush(); }
    //変換
    List<Integer> TOLIST(int [] a) { var List = Arrays.stream(a).boxed().collect(Collectors.toList()); return List; }
    List<Long> TOLIST(long [] a) { var List = Arrays.stream(a).boxed().collect(Collectors.toList()); return List; }
    Set<Integer> TOSET(int [] a) { var List = Arrays.stream(a).boxed().collect(Collectors.toSet()); return List; }
    Set<Long> TOSET(long [] a) { var List = Arrays.stream(a).boxed().collect(Collectors.toSet()); return List; }
    //分布
    int [] COUNT(int [] a) { int [] A = new int[a.length] ; for(int v : a) ++A[v] ; return A ; }
    Map<Long,Integer> COUNT(long [] a) { Map<Long,Integer> C = new HashMap<>(); for(long v : a) C.put(v , C.getOrDefault(v , 0) + 1) ; return C ; }
    //グラフ入力
    <T> List <T> [] GRAPH(int n) { List<T> [] G = new ArrayList[n]; for(int i = 0 ; i < n ; i ++ ) G[i] = new ArrayList<>(); return G ; }
    //個数(二分探索)
    <T extends Comparable<T>> int LOW_(List<T> A , T key) { return upperbound(A, key); }
    <T extends Comparable<T>> int LOW(List<T> A , T key) { return lowerbound(A, key); }
    <T extends Comparable<T>> int HIGH_(List<T> A , T key) { return A.size() - lowerbound(A, key); }
    <T extends Comparable<T>> int HIGH(List<T> A , T key) { return A.size() - upperbound(A, key); }
    <T extends Comparable<T>> int lowerbound(List<T> A, T key) {int left = 0;int right = A.size();while (left < right) {int mid = (left + right) / 2;if (A.get(mid).compareTo(key) < 0) left = mid + 1;else right = mid;}return right;}
    <T extends Comparable<T>> int upperbound(List<T> A, T key) { int left = 0;int right = A.size();while (left < right) {int mid = (left + right) / 2;if (A.get(mid).compareTo(key) <= 0) left = mid + 1;else right = mid;}return right;}
    //定数..
    PrintWriter out = new PrintWriter(System.out);
    In in = new In();
    final long MOD7 = 1000000007;
    final long MOD9 = 998244353;
    final int  inf = (1  << 30);
    final long lnf = (1L << 60);
    final String yes = "Yes";
    final String no  = "No" ;
    final char [] dir = {'U','R','D','L'};
    final int [] dy4 = {-1,0,1,0};
    final int [] dx4 = {0,1,0,-1};
    final int [] dy8 = {-1,-1,-1,0,1,1,1,0};
    final int [] dx8 = {-1,0,1,1,1,0,-1,-1};

}

class CC<T>
{
    TreeSet<T> order ;
    Map<T,Integer> comp ;
    int count ;
    CC(List<T> L)
    {
        this.order = new TreeSet<>(L) ;
        this.comp = new HashMap<>();
        this.count = 0 ;
        for(T v : order) comp.put(v , count++);
    }
    int get(T value) { return comp.get(value); }
}

class In
{

    private final InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private Scanner sc = new Scanner(System.in);
    private int ptr = 0;
    private int buflen = 0;

    private boolean hasNextByte() {
        if (ptr < buflen) {
            return true;
        }else{
            ptr = 0;
            try {
                buflen = in.read(buffer);
            } catch (IOException e) {
                e.printStackTrace();
            }
            if (buflen <= 0) {
                return false;
            }
        }
        return true;
    }

    private int readByte() { 
        if (hasNextByte()) return buffer[ptr++]; else return -1;
    }

    private static boolean isPrintableChar(int c) { 
        return 33 <= c && c <= 126;
    }

    private  boolean hasNext() { 
        while(hasNextByte() && !isPrintableChar(buffer[ptr])) {
            ptr++; 
        }
        return hasNextByte();
    }
    String next() {
        if (!hasNext()) throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while(isPrintableChar(b)) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    long nextLong() {
        if (!hasNext()) throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) {
            throw new NumberFormatException();
        }
        while(true){
            if ('0' <= b && b <= '9') {
                n *= 10;
                n += b - '0';
            }else if(b == -1 || !isPrintableChar(b)){
                return minus ? -n : n;
            }else{
                throw new NumberFormatException();
            }
            b = readByte();
        }
    }

    int nextInt() {
        long nl = nextLong();
        if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
        return (int) nl;
    }

    double nextDouble() { 
        return Double.parseDouble(next());
    }

    char nextChar() {
        return next().charAt(0);
    }
    
    int [] IntArray(int n) {
        final int [] Array = new int [n];
        for(int i = 0 ; i < n ; i ++ ) {
            Array[i] = nextInt();
        }
        return Array;
    }
    int [][] IntArray(int n , int m) {
        final int [][] Array = new int [n][m];
        for(int i = 0 ; i < n ; i ++ ) {
            Array[i] = IntArray(m);
        }
        return Array;
    }   
    long [] LongArray(int n) {
        final long [] Array = new long [n];
        for(int i = 0 ; i < n ; i ++ ) {
            Array[i] = nextLong();
        }
        return Array;
    }
    long [][] LongArray(int n , int m) {
        final long [][] Array = new long [n][m];
        for(int i = 0 ; i < n ; i ++ ) {
            Array[i] = LongArray(m);
        }
        return Array;
    }
    String [] StringArray(int n) {
        final String [] Array = new String [n];
        for(int i = 0 ; i < n ; i ++ ) {
            Array[i] = next();
        }
        return Array;
    }
    char [] CharArray(int n) {
        final char [] Array = new char[n];
        for(int i = 0 ; i < n ; i ++ ) {
            Array[i] = next().charAt(0);
        }
        return Array;
    }
    char [][] CharArray(int n , int m) {
        final char [][] Array = new char [n][m];
        for(int i = 0 ; i < n ; i ++ ) {
            Array[i] = next().toCharArray();
        }
        return Array;
    }
    char [][] CharArray2(int n , int m) {
        final char [][] Array = new char [n][m];
        for(int i = 0 ; i < n ; i ++ ) {
            for(int j = 0 ; j < m ; j ++ ) {
                Array[i][j] = next().charAt(0);
            }
        }
        return Array;
    }
    BigInteger nextBigInteger() {
        return sc.nextBigInteger();
    }
}