  This paper is concerned with the existence of consecutive pairs and
consecutive triples of multiplicatively dependent integers. A theorem by
LeVeque on Pillai's equation implies that the only consecutive pairs of
multiplicatively dependent integers larger than 1 are $(2,8)$ and $(3,9)$. For
triples, we prove the following theorem: If $a\notin \{2,8\}$ is a fixed
integer larger than 1, then there are only finitely many triples $(a,b,c)$ of
pairwise distinct integers larger than 1 such that $(a,b,c)$, $(a+1,b+1,c+1)$
and $(a+2,b+2,c+2)$ are each multiplicatively dependent. Moreover, these
triples can be determined effectively.
