T = int(input())
import math
def is_ok(x,a,b,k): # xに対して、aでもbでも割り切れない数がk個以上存在すればTrue
    g = math.gcd(a, b)
    L = a // g * b
    cnt = x - (x // a) - (x // b) + (x // L)
    return cnt >= k

for _ in range(T):
    A,B,K = map(int,input().split())
    ok = 10 ** 19
    ng = 0
    while abs(ok - ng) > 1:
        mid = abs(ok + ng) // 2
        if is_ok(mid, A, B, K):
            ok = mid
        else:
            ng = mid
    print(ok)