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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 тИТ 5 is divisible by 8, 12 and 15. LCM of 8, 12 and 15: 8 = 2┬│ 12 = 2┬▓ ├Ч 3 15 = 3 ├Ч 5 LCM = 2┬│ ├Ч 3 ├Ч 5 = 8 ├Ч 3 ├Ч 5 = 120 So, N тИТ 5 = 120k тЗТ N = 120k + 5 We need N > 100. For k = 1: N = 120 ├Ч 1 + 5 = 125 (> 100)

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