## https://yukicoder.me/problems/no/573

def calc_gcd(A, B):
    """
    正の整数A, Bの最大公約数を計算する
    """
    a = max(A, B)
    b = min(A, B)
    while a % b > 0:
        c = a % b
        a = b
        b = c
    return b

def func(value, A, B, lcm, K):
    a = value // A
    b = value // B
    l = value // lcm
    x = value - a - b + l
    return x >= K


def solve(A, B, K):
    gcd = calc_gcd(A, B)
    lcm = (A // gcd) * B

    low = 2
    high = 2 * (10 ** 18)
    while high - low > 1:
        mid = (high  + low) >> 1
        if func(mid, A, B, lcm, K):
            high = mid
        else:
            low = mid
    if func(low ,A, B, lcm, K):
        return low
    else:
        return high




def main():
    T = int(input())
    answers = []
    for _ in range(T):
        A, B, K = map(int, input().split())
        ans = solve(A, B, K)
        answers.append(ans)

    for ans in answers:
        print(ans)


if __name__ == '__main__':
    main()