mod = 998244353


def main():
    import sys
    from math import gcd
    input = sys.stdin.readline

    # sum([(a * i + b) // m for i in range(n)])
    def floor_sum(n, m, a, b):
        ret = 0
        while True:
            ret += (a // m) * n * (n - 1) // 2 + (b // m) * n
            a %= m
            b %= m
            y = (a * n + b) // m
            x = b - y * m
            if y == 0:
                return ret
            ret += (x // a + n) * y
            n, m, a, b = y, a, m, x % a

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

        k0 = floor_sum(q, q, p, p) + q - 1
        if k >= k0:
            ans = p * q + (k - k0)
            print(ans * g)
        else:
            ok = p * q
            ng = 0
            mid = (ok + ng) // 2
            while ok - ng > 1:
                x0 = mid // p
                tmp = floor_sum(x0+1, q, p, mid - p * x0) + x0
                if tmp >= k:
                    ok = mid
                else:
                    ng = mid
                mid = (ok + ng) // 2
            print(ok)


if __name__ == '__main__':
    main()