import math

T = int(input())

while T > 0:
    a, b, k = map(int, input().split())
    
    l = 1
    r = 10 ** 25
    
    while r - l > 1:
        mid = (l + r) // 2
        sum = 0
        sum += mid // a
        sum += mid // b
        sum -= mid // (a * b // math.gcd(a, b))
        
        if sum >= k:
            r = mid
        else:
            l = mid
    
    print(r)
    T -= 1