import math

def lcm(a, b):
    return a * b // math.gcd(a, b)

def kth(A, B, K):
    gcd_AB = math.gcd(A, B)
    high = K * (A // gcd_AB + B // gcd_AB)
    low = 1  
    
    while low < high:
        mid = (low + high) // 2
        count = mid - (mid // A) - (mid // B) + (mid // lcm(A, B))

        if count < K:
            low = mid + 1
        else:
            high = mid

    return low
T = int(input())
for _ in range(T):
    A, B, K = map(int, input().split())
    print(kth(A, B, K))