If M = {x : x ∈ N, x ≤ 50, and x is divisible by both 3 and 5}, then M is:
Answer and explanation
Correct answer: M = {15, 30, 45}
A number divisible by both 3 and 5 must be divisible by their least common multiple, LCM(3, 5) = 15. The positive multiples of 15 that are at most 50 are 15, 30, and 45. Therefore, in roster form, M = {15, 30, 45}. The numbers 3 and 5 separately do not satisfy both conditions, and 60 is excluded because it is greater than 50.
Frequently asked questions
What is the correct answer to this question?
M = {15, 30, 45}
Why is this the correct answer?
A number divisible by both 3 and 5 must be divisible by their least common multiple, LCM(3, 5) = 15. The positive multiples of 15 that are at most 50 are 15, 30, and 45. Therefore, in roster form, M = {15, 30, 45}. The numbers 3 and 5 separately do not satisfy both conditions, and 60 is excluded because it is greater than 50.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
