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Class 10MathematicsSetsOperations on Sets (Union, Intersection, Difference)MediumLevel 10

If \(A=\{x\in\mathbb{N}:x\le 40,\ 4\mid x\}\) and \(B=\{x\in\mathbb{N}:x\le 40,\ 6\mid x\}\), what is \(A\cap B\)?

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Answer and explanation

Correct answer: \(\{12,24,36\}\)

An element in \(A\cap B\) must be divisible by both 4 and 6. Such numbers are multiples of their least common multiple, \(\operatorname{lcm}(4,6)=12\). The positive multiples of 12 not exceeding 40 are 12, 24, and 36. Therefore, \(A\cap B=\{12,24,36\}\), making option A correct.

Tags

setsintersectionmultiplesLCMOperations on Sets (UnionDifference)operations on sets union intersection differenceMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

\(\{12,24,36\}\)

Why is this the correct answer?

An element in \(A\cap B\) must be divisible by both 4 and 6. Such numbers are multiples of their least common multiple, \(\operatorname{lcm}(4,6)=12\). The positive multiples of 12 not exceeding 40 are 12, 24, and 36. Therefore, \(A\cap B=\{12,24,36\}\), making option A correct.

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).

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