MathNet 2018-part-06 — 181 problems (EN–VI) Question 102

For natural number $n$ let $S(n)$ denote sum of its digits. From all pairs of natural numbers $(n, m)$, that satisfy equality $S(n) \cdot S(n+1) \cdots S(n+m) = 2018$, find such, for which sum $n+m$ takes the least possible value.