The largest 4 digit number which can be added to 7249 in order to make the derived number divisible by each of 12,14,21,33 and 54 will be?

• answer is 9383
  Find the LCM of the given numbers.
  12= 2*2*3
  14= 2*7
  21= 3*7
  33= 3*11
  54= 3*2*3*3
  
  Max powers of all prime numbers:
  2=2
  3=3
  7=1
  11=1
  
  LCM=2^2*3^3*7^1*11^1=8316
  
  8316-7249=1067. Thus, if we add 1067 to 7249, the number will be divisible by all the given numbers.
  However, 1067 is not the GREATEST 4-digit number to satisfy the condition.
  
  Next number that will be divisible is:
  1067+8316=9383
  
  Thus, adding 9383 to 7249 will give us a number that will be divisible by all the given numbers PLUS 9383 is the greatest 4-digit number that satisfies this condition.
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