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 of $6$ and $15$:

$\lcm \set {6, 15} = 30$

Hence the result.

$\blacksquare$

Sources

• 1975: T.S. Blyth: Set Theory and Abstract Algebra ... (previous) ... (next): $\S 1$. Sets; inclusion; intersection; union; complementation; number systems: Exercise $2$