import sys
input = sys.stdin.readline
from math import gcd

def check(m, a, b):
    val = m
    val -= m // a + m // b
    lcm = a * b // gcd(a, b)
    return val + m // lcm
    

T = int(input())
for _ in range(T):
    A, B, K = map(int, input().split())
    yes = 3 * K
    no = 0
    while yes - no != 1:
        mid = (yes + no)//2
        if check(mid, A, B) >= K:
            yes = mid
        else:
            no = mid
    print(yes)