The least upper bound property for a poset $S$ can be stated as follows: Every nonempty subset of $S$ that is bounded above has a supremum in $S$.
This is a statement taken from a book. Now consider an example where $S=\mathbb{R}$ (Set of real numbers). Let the non empty subset be $D=[2,5]$. Now it is bounded above but it does not contain a supremum. What is wrong in this?
The set certainly contains $\sup$, namely, $5$. Why do you think it does not contain it?