the least number which when divided by 5 , 67 and 8 leaves a remainder 3 , but when divided by 9 leaves no remainder , is : Answers:	A) 1677	B) 1683	C) 2523	D) 3363	E) none of these

Rationale: solution l . c . m . of 5 , 6 , 7 , 8 = 840 . so , required number is of the form 840 k + 3 . least value of k for which ( 840 k + 3 ) is divisible by 9 is k = 2 . so , required number = ( 840 × 2 + 3 ) = 1683 . answer b
Answer: B