from math import gcd, lcm


# n 以下の k の倍数の個数
def f(n, k):
    return n // k


# n 以下の数のうち、C でも D でも割り切れない数の個数
def g(n, a, b):
    assert a != b
    return n - f(n, a) - f(n, b) + f(n, lcm(a, b))


INF = 1 << 60
T = int(input())
for _ in range(T):
    A, B, K = map(int, input().split())
    if K < A and K < B:
        print(K)
        continue
    lo = 1
    hi = INF
    res = lo
    while lo <= hi:
        m = (lo + hi) // 2
        cnt = g(m, A, B)
        if cnt <= K:
            lo = m + 1
            res = max(res, m)
        else:
            hi = m - 1

    print(res)