VN-TST 1990 Problem 4

Let $T$ be a finite set of positive integers, satisfying the following conditions:

1. For any two elements of $T$ , their greatest common divisor and their least common multiple are also elements of $T$ .
2. For any element $x$ of $T$ , there exists an element $x'$ of $T$ such that $x$ and $x'$ are relatively prime, and their least common multiple is the largest number in $T$ .

For each such set $T$ , denote by $s(T)$ its number of elements. It is known that $s(T) < 1990$ ; find the largest value $s(T)$ may take.