Abstract and Applied Analysis
Volume 2013 (2013), Article ID 218125, 4 pages
http://dx.doi.org/10.1155/2013/218125
Research Article

Note on the Lower Bound of Least Common Multiple

Shea-Ming Oon

Institute of Mathematical Sciences, University of Malaya, 50603 Kuala Lumpur, Malaysia

Received 1 July 2012; Revised 24 December 2012; Accepted 10 January 2013

Academic Editor: Pekka Koskela

Copyright © 2013 Shea-Ming Oon. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Consider a sequence of positive integers in arithmetic progression with . Denote the least common multiple of by . We show that if , then , and we obtain optimum result on in some cases for such estimate. Besides, for quadratic sequences , we also show that the least common multiple is at least when , which sharpens a recent result of Farhi.