Question 114
Each of the four positive integers $N, N+1, N+2, N+3$ has exactly six positive divisors. There are exactly 20 different positive integers which are exact divisors of at least one of the integers. One of these is 27. Find all possible values of $N$.
(Both 1 and $m$ are counted as divisors of the integer $m$.)
(Both 1 and $m$ are counted as divisors of the integer $m$.)