What is the smallest number which leaves remainder 3 when divided by any of the numbers 5, 6 or 8, but leaves no remainder when it is divided by 9?

603 243 723 360

243

LCM(5, 6, 8) ⇒ LCM = 240 ⇒ required number = 240 + 3 ⇒ 243 243 is also divisible by 9    ∴ 243 is the least number divided by 5, 6, 8 gives remainder 3.