On the sum of digits of the factorial

Let b >= 2 be an integer and denote by s(b)(m) the sum of the digits of the positive integer In when is written in base b. We prove that s(b)(n!) > C-b log n log log log n for each integer n > e(e), where C-b, is a positive constant depending only on b. This improves by a factor log log log n a previous lower bound for sb(n!) given by Luca. We prove also the same inequality but with n! replaced by the least common multiple of 1, 2, . . . , n. (C) 2014 Elsevier Inc. All rights reserved.