What is the least number which when divided by the number 6, 8, 9, 12, 14 leaves in each case a remainder 2 but when divided by 23 leaves no remainder?

506

1st method - Through option

Check option which is divisible 9 after substract 2 from the option.

Divisibly rule of 9 = Sum of digits are divisible by 9

So ans. option 1 - 506 satisfy, which is also divisible by 23.

2nd method

Required number = (LCM 6, 8, 9, 12, 14) + 2

                          = 504 + 2 = 506, which is also divisible by 23.