This paper is devoted to establish nontrivial effective lower bounds for the least common multiple of consecutive terms of a sequence (u_n)_n∈N whose general term has the form u_n = r(q_n − 1)/(q − 1) + u₀, where r, q and u₀ are non-negative integers satisfying some specific conditions. This can be considered as a q-analog of the lower bounds already obtained by the author (in 2005) and by Hong and Feng (in 2006) for arithmetic progressions.