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Sets & Relations: Multiple Multiple Consists Multiples

JEE Maths question with a full step-by-step solution.

Question
If A={x:x is a multiple of 4}A = \{x : x \text{ is a multiple of } 4\} and B={x:x is a multiple of 6}B = \{x : x \text{ is a multiple of } 6\}, then A∩BA \cap B consists of all multiples of:
A1616
B1212correct
C88
D44
Solution
x∈A∩B⇔xx \in A \cap B \Leftrightarrow x is a multiple of both 44 and 6⇔x6 \Leftrightarrow x is a multiple of lcm⁡(4,6)=12\operatorname{lcm}(4, 6) = 12. ∴A∩B={\therefore A \cap B = \{ multiples of 12}.12 \}. Correct answer: (2)
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