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    Question

    How many numbers in the range from 100 to 800 are

    divisible by 8, 12, and 16?
    A 37 Correct Answer Incorrect Answer
    B 22 Correct Answer Incorrect Answer
    C 25 Correct Answer Incorrect Answer
    D 14 Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    ATQ;

    If a number is a multiple of 8, 12, and 16, then the number is a multiple of the L.C.M of 8, 12, and 16.

    L.C.M of 8, 12, and 16 = 48

    Smallest multiple of 48 between 100 and 800 = 144

    Largest multiple of 48 between 100 and 800 = 768

    Common difference = 48

    Let the required number of terms be 'n'.

    So, 144 + (n - 1) × 48 = 768

    Or, n - 1 = (768 - 144) ÷ 48 = 13

    So, n = 13 + 1 = 14

    So, there are 14 numbers between 100 and 800 which are multiples of 8, 12, and 16.

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