What is the smallest number which leaves remainder 3 when divided by any of the numbers 7, 9 or 10, but leaves no remainder when it is divided by 9?

600 603 610 503

603

LCM(7, 9 and 10) ⇒ LCM = 630 ⇒ required number = 630+ 3 ⇒ 603 603 is also divisible by 9    ∴ 603 is the least number divided by 5, 6, 8 gives remainder 3.