Why is least fixed point (lfp) important in program analysis

Question

I am trying to get a big picture on the importance of least fixed point (lfp) in program analysis. For instance abstract interpretation seems to use the existence of lfp. Many research papers on program analysis also focus heavily on finding least fixed point.

More specifically, this article in wikipedia : Knaster-Tarski Theorem mentions that lfp are used to define program semantics.

Why is it important? Any simple example helps me. (I am trying to get a big picture).

EDIT

I think my wording is incorrect. I donot challenge the importance of lfp. My exact question (beginner) is: How does computing lfp help in program analysis? For e.g., why/how abstract interpretation uses lfp? what happens if there is no lfp in the abstract domain?

Hopefully my question is more concrete now.