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      Question

      Find the smallest number greater than 100 which, when

      divided by 8, 12 and 15, leaves a remainder of 5 in each case.
      A 125 Correct Answer Incorrect Answer
      B 165 Correct Answer Incorrect Answer
      C 142 Correct Answer Incorrect Answer
      D 110 Correct Answer Incorrect Answer

      Solution

      Let the required number be N. N βˆ’ 5 is divisible by 8, 12 and 15. LCM of 8, 12 and 15: 8 = 2Β³ 12 = 2Β² Γ— 3 15 = 3 Γ— 5 LCM = 2Β³ Γ— 3 Γ— 5 = 8 Γ— 3 Γ— 5 = 120 So, N βˆ’ 5 = 120k β‡’ N = 120k + 5 We need N > 100. For k = 1: N = 120 Γ— 1 + 5 = 125 (> 100)

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