ANSWER: Business School = 840, Language School = 910, and Design School = 533.

EXPLANATION:
First we recognize that each school must have an integer number of students - there are no fractional people. Therefore, the business school enrollment must be an integral multiple of 2, 3, 4, 5, 6, 7, and 8. The factors of these numbers are respectively 2, 3, 2x2, 5, 2x3, 7, and 2x2x2. We now find the least common multiple by combining these factors, but only using the 2 three times (this is necessary for the 8 and included in the 2, 4, and 6) and the 3 once (necessary for the six and included in the 3) to yield 2x2x2x3x5x7=840.

We then can compute the respective fractions of the business school to give the enrollments for the Language and Design Schools. 1/2, 1/3, and 1/4 of 840 is 420, 280 and 210 respectively.

Therefore, the Language School enrollment is 420 + 280 + 210=910. Similarly, 1/5, 1/6, 1/7, and 1/8 of 840 is 168, 140, 120, and 105. Therefore, the enrollment of the Design School is 168 + 140 + 120 +1