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    Find the least number which when divided by 8, 12 and 16, leaves three as the remainder in each case but when divided by 7 leaves no remainder.
    Question

    Find the least number which when divided by 8, 12 and 16, leaves three as the remainder in each case but when divided by 7 leaves no remainder.

    A.

    266

    B.

    248

    C.

    147

    D.

    149

    Correct option is C

    Given:

    Divisors: 8, 12, 16.

    Remainder when divided by 8, 12, and 16: 3.

    The number must be divisible by 7.

    Solution:

    L.C.M. of  8, 12, and 16 is 48.

    But, get remainder = 3

    Checking multiples of 48 (accounting for the remainder of 3):

    51 (48 + 3) is not divisible by 7.

    99 (48×2 + 3) is not divisible by 7.

    147 (48×3 + 3) is divisible by 7.

    ∴ The correct answer is 147.

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