If \(A=\{x:x\text{ is a multiple of }3,\ 1\le x\le20\}\) and \(B=\{x:x\text{ is a multiple of }5,\ 1\le x\le20\}\), what is \(A\cap B\)?
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Answer and explanation
Correct answer: \(\{15\}\)
Multiples of 3 from 1 through 20 are \(\{3,6,9,12,15,18\}\), while multiples of 5 are \(\{5,10,15,20\}\). The only number appearing in both lists is 15. Equivalently, the least common multiple of 3 and 5 is 15, and the next common multiple is 30, which exceeds 20. Therefore \(A\cap B=\{15\}\).
Frequently asked questions
What is the correct answer to this question?
\(\{15\}\)
Why is this the correct answer?
Multiples of 3 from 1 through 20 are \(\{3,6,9,12,15,18\}\), while multiples of 5 are \(\{5,10,15,20\}\). The only number appearing in both lists is 15. Equivalently, the least common multiple of 3 and 5 is 15, and the next common multiple is 30, which exceeds 20. Therefore \(A\cap B=\{15\}\).
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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