Digit Cancelling Fractions

The fraction 49/98 is curious: by cancelling the 9 from numerator and denominator, we get 4/8, which equals 49/98. We consider fractions less than 1 with two-digit numerator and denominator. Given max_den, consider all such curious fractions with denominator <= max_den. If the product of all these fractions is given in lowest terms, find the denominator.