Digital compatibility of logic gates
You say you've already checked that the voltages are compatible, so no check the current.  The output can only source or sink some maximum current for the other specs to be valid.  Each input requires some current to hold it in a guaranteed logic high or low condition.  Overall, you have to make sure that the output can source/sink at least the current required by all inputs together.

You have all the values essentially sitting on a silver platter.  Go do the math.