from math import *

t = int(input())

for i in range(t):
    a,b,k = map(int,input().split())
    g = gcd(a,b)
    n = a//g*b
    right = 10**19
    left = 0
    while abs(right-left) > 1:
        mid = (right+left)//2
        if mid-(mid//a)-(mid//b)+(mid//n) >= k:
            right = mid
        else:
            left = mid
            
    print(right)