N is a positive integer ,which when divided by 16 ,17,18 giver remainders of 6,7,8 resp.find the rem when N^2+5N+6 is divided by 12

• N is 4886 .
  
  4886^2 +5*4886 +6 = 358094940 + 24430 +6 = 358119396 which is fully divisible by 12.
  
  so remainder is zero.
• 13 years agoHelpfull: Yes(2) No(4)
• L.C.M of 16,17,18 is 2448.to get remainders of 6,7,8 subtract 10 from L.C.M which is 2438.
  so required num is 2438.
  factorizing equation we get (N+2)(N+3)
  substituting we get 2440*2441
  on simplification we get 610*2441/3=>1*1/3=>remainder=1
  as we cancelled 4 times remainder is 4.
• 10 years agoHelpfull: Yes(0) No(0)
• There is a small mistake in Mr. Ramani answer. I have corrected it.
  
  L.C.M of 16,17,18 is 2448.to get remainders of 6,7,8 subtract 10 from L.C.M which is 2438.
  so required num is 2438.
  factorizing equation we get (N+2)(N+3)
  substituting we get 2440*2441
  on simplification we get 610*2441/3=>1*2/3=>remainder=2
  as we cancelled 4 times remainder is 2*4 = 8.
  
  or..
  Don't cancel the 4.
  R [2440/12]* R [2441/12] = 4 * 5 = 20 => r [20/12] = 8 (Ans)
• 7 years agoHelpfull: Yes(0) No(0)