Question:
If \( A = \{ x : x { is a multiple of 4} \} \) and \( B = \{ x : x { is a multiple of 6} \} \), then \( A \cap B \) consists of multiples of:
If \( A = \{ x : x { is a multiple of 4} \} \) and \( B = \{ x : x { is a multiple of 6} \} \), then \( A \cap B \) consists of multiples of:
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To find the intersection of two sets of multiples, calculate the least common multiple (LCM) of the numbers. The intersection will consist of all multiples of the LCM.
Updated On: Feb 4, 2025
- 16
- 12
- 8
- 4
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The Correct Option is B
Solution and Explanation
The set \( A \) consists of all multiples of 4, i.e., \( A = \{ 4, 8, 12, 16, 20, \dots \} \).
The set \( B \) consists of all multiples of 6, i.e., \( B = \{ 6, 12, 18, 24, 30, \dots \} \).
The intersection of sets \( A \) and \( B \), denoted as \( A \cap B \), consists of all elements that are common to both sets.
To find the common multiples of 4 and 6, we need to find the least common multiple (LCM) of 4 and 6.
The LCM of 4 and 6 is 12. Therefore, \( A \cap B \) consists of all multiples of 12. Thus, the correct answer is Option B (12).
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