from math import gcd
def solve():

    a,b,k = map(int,input().split())
    ab = a*b//(gcd(a,b))
    l = k-1
    r = 10**22

    while r - l > 1:

        m = (r+l)//2

        num = m

        num -= m//a + m//b
        num += m//ab

        if num > k:
            r = m
        else:
            l = m

    return l

t = int(input())
for _ in range(t):
    print(solve())