A lattice is a partially ordered set, or poset.

Here is a lattice ordered by divisibility:

See other examples.

Every two elements of a lattice has:

• a supremum, or least upper bound, or join. e.g. LCM
• an infimum, or greatest lower bound, or meet. e.g. GCD

References

https://en.wikipedia.org/wiki/Lattice_(order)