Intersection of Sets of Integer Multiples/Examples/2 Z cap 7 Z

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

Then:
 * $2 \Z \cap 7 \Z = 14 \Z$

Proof
From Intersection of Sets of Integer Multiples


 * $2 \Z \cap 7 \Z = \lcm \set {2, 7} \Z$

We have that:
 * $2 \perp 7$

where $\perp$ denotes coprimality.

Then from LCM equals Product iff Coprime:
 * $\lcm \set {2, 7} = 2 \times 7 = 14$

Hence the result.