Which is the set X = {x ∈ ℕ : x is a multiple of both 4 and 6 and x < 30}?
Answer and explanation
Correct answer: {12, 24}
A number that is a multiple of both 4 and 6 must be a multiple of their least common multiple. Since lcm(4, 6) = 12, the common multiples below 30 are 12 and 24. The number 36 is already beyond the bound. Thus the required set is X = {12, 24}. Option D lists multiples of 6 but incorrectly includes numbers that are not multiples of 4.
Frequently asked questions
What is the correct answer to this question?
{12, 24}
Why is this the correct answer?
A number that is a multiple of both 4 and 6 must be a multiple of their least common multiple. Since lcm(4, 6) = 12, the common multiples below 30 are 12 and 24. The number 36 is already beyond the bound. Thus the required set is X = {12, 24}. Option D lists multiples of 6 but incorrectly includes numbers that are not multiples of 4.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
