How to prove that Dn, a set of all positive divisors of n under the relation of divisibility, is a lattice?

Question

show that D72 is a lattice

The solution I can come up is first prove that the set with the given relation (divisibility) is a partial order and then show that for every possible pairs there exists a greatest lower bound and least upper bound.

Surely this is not the right way to go as for larger values of n it'll be impossible to prove.

Answer 1

The infinum is the greatest common factor.
The supremum is the least common multiple.