Civil Services Examination · Question 59
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.
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Answer: (C) Both I and II
Explanation
HCF × LCM = ab = a³, so b = a². Then b is a perfect square, and b - a = a(a - 1), a product of consecutive integers, which is even.