Consider the poset $\left({3,5,9,15,24,45}, \mid\right)$.

Which of the following is correct for the given poset?

In divisibility poset, least element means an element which divides every element.

Here, $3$ does not divide $5$, so $3$ is not the least element.

Similarly, no other element divides all elements of the set.

So, least element does not exist.

Greatest element means an element which is divisible by every element.

Here, $45$ is not divisible by $24$.

Also, no other element is divisible by all elements of the set.

So, greatest element does not exist.

Therefore, there does not exist a greatest element and a least element.