There is a set called X;
X = { 2, 5, 15, 40, 120, 111, 140 }
And I drew the divisibility hasse diagram of this set.
I know 120 and 140 are maximals, 2 and 5 are minimals, minimum and maximum dont exist. But I am not sure about is 111 maximal or minimal or both. Because 111 fulfill the definitions of maximal and minimal at the same time.
As you note the number $111$ fulfills both definitions, and hence it is both minimal and maximal.