import std;

void main () {
    int T = readln.chomp.to!int;
    foreach (_; 0..T) {
        int A, B;
        long K;
        readln.read(A, B, K);
        auto ans = solve(A, B, K);
        writeln(ans);
    }
}

auto solve (int A, int B, long K) {
    /* 二分探索 */
    long LCM = lcm(A, B);
    bool f (long x) {
        return (x - x/A - x/B + x/LCM) <= K;
    }

    long ok = 0, ng = 9*10L^^18;
    while (1 < abs(ok-ng)) {
        long mid = (ok+ng) / 2;
        if (f(mid)) {
            ok = mid;
        } else {
            ng = mid;
        }
    }

    return ok;
}

long gcd (long A, long B) {
    enforce(0 <= A && 0 <= B);
    enforce(!(A == 0 && B == 0));

    while (0 < A) {
        long tmp = A;
        A = B % A;
        B = tmp;
    }
    return B;
}

long lcm (long A, long B) {
    return A/gcd(A, B)*B;
}

void read(T...)(string S, ref T args) {
    auto buf = S.split;
    foreach (i, ref arg; args) {
        arg = buf[i].to!(typeof(arg));
    }
}