  In a recent paper the author derived a formula for calculating common denominators for the homogeneous components of the Baker-Campbell-Hausdorff (BCH) series. In the present work it is proved that this formula actually yields the smallest such common denominators. In an appendix a new efficient algorithm for computing coefficients of the BCH series is presented, which is based on these common denominators, and requires only integer arithmetic rather than less efficient rational arithmetic. 
Smallest common denominators for the homogeneous components of the   Baker-Campbell-Hausdorff series