Can you find out the remainder when 3^300 is divided by 5?

Question

Can you find the least possible number such that

If the number is divided by 3, it gives the remainder of 1;
If the number is divided by 4, it gives the remainder of 2;
If the number is divided by 5, it gives the remainder of 3;
If the number is divided by 6, it gives the remainder of 4.

Answer 1

3^4 mod 5 = 81 mod 5 = 1
3^300 mod 5 = (3^4)^75 mod 5 = (3^4 mod 5)^75 mod 5 = 1