Find the least common multiple of k,k+1, and k+2 where k≡3(mod 4).

Some ideas:

k≡3(mod 4) => k=3+4z for some z E Z

So k is odd, k+1 is even, and k+2 is odd.

Also, this question asks about the lcm of THREE numbers, so I don't think the the Euclidean algorithm (which only gives the gcd or lcm of TWO numbers) will help us in this question.

So how can we solve this?

Thanks for any help!

[also under discussion in math links forum]