187 Rectangles

I felt bad leaving you people with nothing to read, so I decided to throw in a little problem for you to solve in the meantime. This problem is known as the Integers and Rectangles Problem.

Integers & Rectangles

A large rectangle is made out of smaller rectangles of different lengths and breadth. However, all the small rectangles either have an integer length or breadth, (or both). For example, one possible rectangle may be 3 cm x 2.4 cm, or perhaps 4.1 cm x 2 cm, or even 3 cm x 1 cm. Your problem is this:

Prove that the large rectangle (made from the smaller rectangles) also have this property, i.e. integer length or breadth.