What is the smallest number that has above properties?

A number has a remainder of 1 when divided by 4, a remainder of 2 when divided by 5 and a remainder of 3 when divided by 6. What is the smallest number that has above properties?

Let N be the number.

(1) N/4 gives a remainder of 1 => N+3 divisible by 4
(2) N/5 gives a remainder of 2 => N+3 divisible by 5
(3) N/6 gives a remainder of 3 => N+3 divisible by 6

From the above conclusions, N+3 should be divisible by 4, 5 and 6.
The lowest common multiple of 4, 5 and 6 is 60.

i.e; N+3 = 60
N=57.

The smallest number with the mentioned properties is 57.