If the product of the HCF and LCM of two distinct numbers is the cube of one of the numbers, then which of the following statements is/are correct?
I. The difference of the numbers is an even number. II. One of the numbers is a perfect square.
Select the answer using the code given below.
Detailed Explanation:
Let two distinct numbers be a and b. Using HCF × LCM = a × b, and given this product equals the cube of one number (say a³): a × b = a³, so b = a².
Statement I: Difference = a² − a = a(a − 1), the product of two consecutive integers, which is always even. ✓
Statement II: One number is a², which is a perfect square. ✓
Therefore, both statements I and II are correct, making Option 3 the correct answer.
Question 3 of 7 HCF and LCM
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