[cl3misch]

Thanks, that was fun.

    def d(x): N = arange(1, x + 1); return N[x % N == 0]
    def m(x, n): return x * arange(1, n + 1)
    def gcd(x, y): return max(set(d(x)) & set(d(y)))
    def lcm(x, y): return min(set(m(x, y)) & set(m(y, x)))
    def test(x, y): return gcd(x, y) * lcm(x, y) == x * y
    all([test(x, y) for (x, y) in randint(1, 100, (1000, 2))])  # True

I am not a good golfer. Now I want to look at the codegolf stackexchange for this...