from math import gcd


def solve():
    A, B, K = map(int, input().split())
    L = A * B // gcd(A, B)
    lo = 0
    hi = 10 ** 19
    while hi - lo > 1:
        md = (hi + lo) // 2
        cnt = md - md // A - md // B + md // L
        if cnt >= K:
            hi = md
        else:
            lo = md
    print(hi)

T = int(input())
for _ in range(T):
    solve()