Dutch Mathematical Olympiad

A teacher makes a big fraction with the numbers $1$ up to and including $12$. She writes some of the numbers in the numerator and puts $\times$-signs between them. She puts the remaining numbers in the denominator, again with $\times$-signs between the numbers. In both the numerator and denominator, there is at least one number. She makes sure that the fraction equals an integer that is as small as possible. What is this integer?