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      Question

      Let тАШxтАЩ be the least number divisible by 9, 12, 16,

      18 and 20, and also тАШxтАЩ is a perfect square. Find the remainder when тАШxтАЩ is divided by 95.
      A 20 Correct Answer Incorrect Answer
      B 71 Correct Answer Incorrect Answer
      C 85 Correct Answer Incorrect Answer
      D 54 Correct Answer Incorrect Answer

      Solution

      ATQ, LCM of 9, 12, 16, 18 and 20 = 720 Since, 720 = (2 ├Ч 2 ├Ч 2 ├Ч 2 ├Ч 3 ├Ч 3 ├Ч 5) To make it a perfect square, multiply by тАШ5тАЩ. So, desired number = 720 ├Ч 5 = 3600 3600 ├╖ 95 = 37 ├Ч 95 + 85 So, desired remainder = 85

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