Comparing cells and result enters the lower value

I have:
Column A
Column B
Column C

Column A and B have two different values or the same value.
I would like Column C to compare Columns A to B.
If Column A is the smaller cell enter that value in C
If Column B is smaller cell enter that value in C
If Column A and B are the same value, enter that value in C.

What is the formula to be entered in C?

V. Ouellette

=MIN(A1,B1) copied down...