from math import lcm
for _ in range(int(input())):
    a,b,k = map(int,input().split())
    m = lcm(a,b); ng = 0; ok = 3*10**18
    while ok-ng>1:
        mid = (ng+ok)//2
        if mid-(mid//a+mid//b-mid//m)>=k: ok = mid
        else: ng = mid
    print(ok)