Firstly, we need to find how many cups of butter is needed to bake [tex]15[/tex] batches. We will need [tex]15 \cdot \frac{3}{8} = \frac{45}{8}[/tex] cups of butter. This is [tex]5.625[/tex] cups. Since we can only buy butter in boxes with 2 cups of butter in it, we will have to buy 3. This will give us 6 cups of butter, which will be enough. If we only buy 2, then we will only have 4 cups of butter, which won't be enough to bake 15 batches of cookies.
So, the answer is [tex]\boxed{3}.[/tex]
