The lcd of two fractions is always greater than the denominator of the fractions. reasonable or not?

It is not reasonable.
The LCD can be less than the denominators if the fractions are not in simplest form but the LCD can be equal to one of the fractions even if they are in simplest form, for example:
3/4 and 1/2

Hope this helps :)

Lcd means least common denomenators
it is normally used to combine fractions with differnt denomenators

I can show 2 disproofs

so
they can be equal
conside
3/4 and 5/8
lcd is 8, 8>8 is false
not reasnable

they can be less if they arenot simplified
example
4/8 and 24/16
lcd is 4

not reasonable

No solution : there is no number of boxes that she bought