from math import lcm

T = int(input())

def func(n):
    return n-n//A-n//B+n//LCM

for _ in range(T):
    A, B, K = map(int, input().split())
    LCM = lcm(A, B)
    left = 0
    right = 10**18*6
    while left+1 < right:
        mid = (left+right)//2
        if func(mid) < K:
            left = mid
        else:
            right = mid
    print(right)