If V = {x : x ∈ N, x is a common multiple of 9 and 12, and x ≤ 100}, what is V?
Advertisement
Answer and explanation
Correct answer: V = {36, 72}
A common multiple of 9 and 12 must be a multiple of their least common multiple. Since 9 = 3² and 12 = 2² × 3, LCM(9, 12) = 2² × 3² = 36. The positive multiples of 36 not exceeding 100 are 36 and 72; the next one, 108, is too large. Therefore V = {36, 72}, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
V = {36, 72}
Why is this the correct answer?
A common multiple of 9 and 12 must be a multiple of their least common multiple. Since 9 = 3² and 12 = 2² × 3, LCM(9, 12) = 2² × 3² = 36. The positive multiples of 36 not exceeding 100 are 36 and 72; the next one, 108, is too large. Therefore V = {36, 72}, so option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
Advertisement