Intersection of Sets of Integer Multiples/Examples/6 Z cap 15 Z

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

Then:
 * $6 \Z \cap 15 \Z = 30 \Z$

Proof
From Intersection of Sets of Integer Multiples


 * $6 \Z \cap 15 \Z = \lcm \set {6, 15} \Z$

From Lowest Common Multiple/Examples/6 and 15:
 * $\lcm \set {6, 15} = 30$

Hence the result.