Question 4
A finite set $T$ of positive integers satisfies:
1. For any two elements of $T$, their greatest common divisor and least common multiple also belong to $T$.
2. For every $x\in T$, there is $x'\in T$ such that $\gcd(x,x')=1$ and $\operatorname{lcm}(x,x')$ is the largest element of $T$.
Write $l(T)$ for the number of elements. Find its greatest possible value subject to $l(T)\lt1990$.
1. For any two elements of $T$, their greatest common divisor and least common multiple also belong to $T$.
2. For every $x\in T$, there is $x'\in T$ such that $\gcd(x,x')=1$ and $\operatorname{lcm}(x,x')$ is the largest element of $T$.
Write $l(T)$ for the number of elements. Find its greatest possible value subject to $l(T)\lt1990$.