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    Determine the smallest number which when divided by 12,16,20,25 and 30 leaves the same remainder 3 in each case.
    Question

    Determine the smallest number which when divided by 12,16,20,25 and 30 leaves the same remainder 3 in each case.

    A.

    1023

    B.

    1203

    C.

    1303

    D.

    1233

    Correct option is B

    Concept used:

    When smallest number asked, which when divided by a, b, c leaves the same remainder R in each case, that number is LCM[a, b, c] + R

    Solution:

    ∴ Smallest number which when divided by 12,16, 20.25 and 30 leaves the same remainder 3 in each case is LCM[12,16, 20.25, 30] + 3

    = 1200 + 3

    = 1203

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