Intersection of Sets of Integer Multiples/Examples/(3 Z cap 6 Z) cup 18 Z

Examples of Use of Intersection of Sets of Integer Multiples
Let $m \Z$ denote the set of integer multiples of $m$.

Then:
 * $\paren {3 \Z \cap 6 \Z} \cup 18 \Z = 6 \Z$

Proof
From Intersection of Sets of Integer Multiples:


 * $3 \Z \cap 6 \Z = \lcm \set {3, 6} \Z = 6 \Z$

Then we have that:
 * $18 \Z \subseteq 6 \Z$

and so from Union with Superset is Superset:
 * $6 \Z \cup 18 \Z = 6 \Z$

Hence the result.