from math import gcd

def solve(p, q, k):
    x = p * q
    y = (p - 1) * (q - 1)
    if y <= k:
        ans = x - 1 + k - y
        return ans

    if p > q:
        p, q = q, p
    
    ma = k // q
    lst = [q]
    se = {0}
    tot = 0
    for _ in range(ma + 10):
        tot += p
        if (tot % q) not in se:
            lst.append(tot)
            se.add(tot % q)    

    def cnt(x):
        c = 0
        for a in lst:
            c += max(0, (x - a + q) // q)
        return c

    l = 0
    r = p * q
    while r - l > 1:
        mid = (l + r) // 2
        if cnt(mid) >= k:
            r = mid
        else:
            l = mid
    return r


for _ in range(int(input())):
    p, q, k = map(int, input().split())
    g = gcd(p, q)
    p //= g
    q //= g
    print(g * solve(p, q, k))