Intersection of Sets of Integer Multiples/Examples/6 Z cap 15 Z
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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 $2$