a, b, c, d are positive integers. If a/b has a remainder of 9 and c/d has a remainder of 10, what is the minimum possible value of b*d?

Answer key says 110.. I disagree, can someone explain why the following is not true:

If a = 1, c = 1
b = 9, d = 10 for an answer of 90.

1/9 = remainder of 9
1/10 = remainder of 10

Why, "the remainder must always be smaller than the divisor"? If the numerator is smaller than the divisor, doesn't the divisor = the remainder?