import math

def gcd(a, b):
    return math.gcd(a, b)

def judge(X, A, B, C, K):
    return X - (X//A + X//B - X//C) <= K

def solve():
    A, B, K = map(int, input().split())
    assert A != B
    assert 2 <= A <= 1e9
    assert 2 <= B <= 1e9
    assert 1 <= K <= 1e18
    C = A * B // gcd(A, B)

    l = int(0)
    r = int(4e18)
    while r - l > 1:
        c = (l + r) // 2
        if judge(c, A, B, C, K):
            l = c
        else:
            r = c

    l = int(l)
    mi = max(1, l - 5)
    for X in range(mi, l + 1):
        if X - (X//A + X//B - X//C) == K and X % A != 0 and X % B != 0:
            print(X)
            return

    assert False

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