from math import gcd
t = int(input())
for i in range(t):
    a, b, k = map(int, input().split())
    l, r = 0, 10 ** 19 + 1
    while r - l > 1:
        m = (l + r) // 2
        x = m - (m // a + m // b - m // (a * b // gcd(a, b)))
        if x >= k:
            r = m
        else:
            l = m
    print(r)