What is the smallest number which leaves remainder 3 when

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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 ?

1. 123
2. 603
3. 723
4. 243

Correct Option: D

We find LCM of 5, 6 and 8
5 = 5
6 = 3 × 2
8 = 2³
LCM of 5, 6 and 8 = 2³ × 3 × 5 = 8 × 15 = 120
Required number = 120K + 3
when K = 2,
∴ Required number = 120 × 2 + 3 = 243
It is completely divisible by 9