from math import gcd

## sum_{i=0}^{n-1}{(i*a + b)//m}
def floor_sum(n, m, a, b):
    ans = 0
    while True:
        if a >= m or a < 0:
            ans += n * (n - 1) * (a // m) // 2
            a %= m
        if b >= m or b < 0:
            ans += n * (b // m)
            b %= m
        y_max = a * n + b
        if y_max < m: break
        n, b, m, a = y_max // m, y_max % m, a, m
    return ans 



def count_ok(p, q, x):
    # sum_{i=0}^{q-1}((x-i*p)//q + 1) - 1
    # ただし、 x-i*p >= 0 <=> i <= x // p
    n = min(q, x//p + 1)
    return floor_sum(n, q, -p, x) + n - 1


def solve():
    P, Q, K = map(int, input().split())
    g = gcd(P, Q)
    p = P // g
    q = Q // g
    if 1 in (p, q) and K == 1:
        return g
    
    ng = 1
    ok = P*K
    while ng+1 < ok:
        mid = (ng + ok) // 2
        cnt = count_ok(p, q, mid)
        # print(f'{p = }, {q = }, {mid = }')
        # print(f'{cnt = }')
        if cnt >= K:
            ok = mid
        else:
            ng = mid
    return ok * g


T = int(input())

for _ in range(T):
    res = solve()
    print(res)