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
    
    dp = [0] * p
    tot = 0
    for _ in range(p - 1):
        tot += q
        dp[tot % p] = tot
    dp[0] = p

    def cnt(x):
        t = 0
        for a in dp:
            t += max(0, (x - a + p) // p)
        return t

    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))