When n is divided by 2, the remainder is 1.
When n is divided by 3, the remainder is 2.
When n is divided by 4, the remainder is 3.
When n is divided by 5, the remainder is 4.
When n is divided by 6, the remainder is 5.
LCM[2, 3, 4, 5, 6] = 60
n =60m + 59, where m =0, 1, 2, 3, 4......etc.
So, the smallest n = 59.