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Class 10MathematicsSetsThe Empty Set, Finite and Infinite Sets, Equal SetsMediumLevel 2

How many elements are in A = {x : x ∈ ℕ, x is a multiple of both 12 and 18 and x < 100}?

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Answer and explanation

Correct answer: 2

A number that is a multiple of both 12 and 18 must be a multiple of their least common multiple. Since lcm(12, 18) = 36, the positive multiples below 100 are 36 and 72. The next multiple, 108, is not less than 100. Therefore, A = {36, 72} and has 2 elements, so option B is correct.

Tags

setscommon-multipleslcmThe Empty SetFinite and Infinite SetsEqual Setsthe empty set finite and infinite sets equal setsMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

2

Why is this the correct answer?

A number that is a multiple of both 12 and 18 must be a multiple of their least common multiple. Since lcm(12, 18) = 36, the positive multiples below 100 are 36 and 72. The next multiple, 108, is not less than 100. Therefore, A = {36, 72} and has 2 elements, so option B is correct.

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Sets. Topic: The Empty Set, Finite and Infinite Sets, Equal Sets.

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