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UPSC PYQPrelims 2026

Civil Services Examination · प्रश्न 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.

  1. I only
  2. II only
  3. Both I and II
  4. Neither I nor II
उत्तर देखें और व्याख्या

उत्तर: (C) Both I and II

व्याख्या

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.