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Let us draw the Hasse diagram of lattices, and where and and a < b if and only if a divides b.
Note that a Hasse diagram is a graphical rendering of a partially ordered set displayed via the cover relation of the partially ordered set with an implied upward orientation. A point is drawn for each element of the poset, and line segments are drawn between these points according to the following two rules:
1. If in the poset, then the point corresponding to appears lower in the drawing than the point corresponding to .
2. The line segment between the points corresponding to any two elements and of the poset is included in the drawing iff covers or covers .
In our case, if and only if Therefore, the Hasse diagrams are the following: