MathematicsFind the least number which when divided by 16 leaves a remainder 6, when divided by 19 leaves a remainder 9 and when divided by 21 leaves a remainder 11.

Find the least number which when divided by 16 leaves a remainder 6, when divided by 19 leaves a remainder 9 and when divided by 21 leaves a remainder 11.


  1. A
    6374
  2. B
    5461
  3. C
    2145
  4. D
    6231 

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    Solution:

    It is given that, when a number divided by 16 leaves the remainder 6 when divided by 19 leaves the remainder 9 when divided by 21 leaves the remainder 11.
    Then, suppose that number is a  .
    When the number is divisible by 16 then exactly it divisible by,
    ⇒16−6=10  
    When the number is divisible by 19 then exactly it divisible by,
    ⇒19−9=10  
    Similarly, when the number is divisible by 21 then exactly it divisible by,
    ⇒21−11=10  
    The LCM of the numbers are,
    ⇒LCM=16×19×21 ⇒LCM=6384  
    Thus, the required number will be,
    ⇒a=LCM−10 ⇒a=6384−10 ⇒a=6374  
    Hence the required number is 6374.
    Therefore the correct answer is option (1).
     
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