On the other hand, we can get quite nice [graded lattices](https://en.wikipedia.org/wiki/Graded_poset) out of the divisibility relation. For better or for worse, these are usually what I visualize when I think of lattices.

[![Divisibility lattice](https://i.stack.imgur.com/k6oX5.jpg)](https://math.stackexchange.com/a/1838291)