from math import gcd


def solve(a, b, k):
    l = 0
    r = k * 7
    lc = a * b // gcd(a, b)
    while r - l > 1:
        m = (l + r) // 2
        c = m // a + m // b - m // lc
        if m - c >= k:
            r = m
        else:
            l = m

    return r


for _ in range(int(input())):
    print(solve(*map(int, input().split())))