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6th Class Mathematics Playing with Numbers Question Bank Playing with Numbers

  • question_answer
    The smallest number which when divided by 20, 25, 35 and 40 leaves a remainder of 14, 19, 29 and 34 respectively, is _________.

    A)  1394

    B)  1404

    C)  1664

    D)  1406

    Correct Answer: A

    Solution :

    The smallest number which is exactly divisible by 20, 25, 35 and 40 is their LCM. \[\therefore \] LCM \[=2\times 2\times 2\times 5\times 5\times 7\] \[=1400\]
    2 20, 25, 35, 40
    2 10, 25, 35, 20
    2 5, 25, 35, 10
    5 5, 25, 35, 5
    5 1, 5, 7, 1
    7 1, 1, 7, 1
    1, 1, 1, 1
    \[\therefore \] Required number will be 6 less than LCM = 1400 - 6 = 1394


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