Question:
\(N\) denotes the set of all natural numbers. Define, for \(a \in N\)
\[
aN=\{ax:x\in N\}
\]
Then
\[
5N \cap 3N=
\]
\(N\) denotes the set of all natural numbers. Define, for \(a \in N\)
\[
aN=\{ax:x\in N\}
\]
Then
\[
5N \cap 3N=
\]
Show Hint
The intersection of \(aN\) and \(bN\) is always the set of multiples of \(\text{LCM}(a,b)\).
Updated On: Jul 15, 2026
- \(5N\)
- \(3N\)
- \(15N\)
- \(\emptyset\)
Show Solution
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The Correct Option is C
Solution and Explanation
Concept:
Intersection means common elements.
\[
5N=\{5,10,15,20,25,\dots\}
\]
\[
3N=\{3,6,9,12,15,18,21,\dots\}
\]
Step 1: Find common multiples.
Common elements are: \[ 15,30,45,60,\dots \] These are exactly the multiples of: \[ LCM(5,3)=15 \] So: \[ 5N\cap 3N=15N \] Thus, the required answer is: \[ \boxed{15N} \]
Step 1: Find common multiples.
Common elements are: \[ 15,30,45,60,\dots \] These are exactly the multiples of: \[ LCM(5,3)=15 \] So: \[ 5N\cap 3N=15N \] Thus, the required answer is: \[ \boxed{15N} \]
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