Which of the following represents the largest 4 digit number which can be added to 7855 in order to make the derived number divisible by each of the following numbers 12,14,21,33 and 54?

• 12(2*2*3),14(2*7),21(3*7),33(3*11),54(2*3*3*3)
  LCM OF 12,14,21,33,54 IS=2 x 2 x 3 x 3 x 3 x 7 x 11 = 8316.
  So, 8316 - 7855 = 461 is the number you have to add to 7355 so that it is divisible by these 5 numbers.
• 5 years agoHelpfull: Yes(2) No(3)
• 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.
  
  Ans: "B"
• 5 years agoHelpfull: Yes(0) No(0)
• LCM of 5 no= 8316
  so largest 4 digit number to be added is: 2*8316- 7855= 8777 (Ans)
• 5 years agoHelpfull: Yes(0) No(0)