The expression x#y denotes the product of the consecutive multiples of 3 between x and y, inclusive. What is the sum of the exponents in the prime factorization of 21#36?
Select the correct option
A) 16 B) 17 C) 18 D) 19 E) 20
First, let's translate the expression 21#36, using the definition given:   21#36 = 21×24×27×30×33×36   We need the prime factorization of this product.   Let's factor out 3 from each multiple.   21#36 = 3^6(7×8×9×10×11×12)   Now let's replace each consecutive integer with its prime factorization:   21#36 = 3^6(7×2^3×3^2×(2×5)×11×(2^2×3))   Let's group the prime bases:   21#36 = 2^6×3^9×5×7×11   The sum of the exponents is  6 + 9 + 1 + 1 + 1= 
<gadget id="calculator"> 6 + 9 + 1 + 1 + 1</gadget>
<output>18</output>
18   The answer is 18.
<result>C</result>
The expression x#y denotes the product of the consecutive multiples of 3 between x and y, inclusive. What is the sum of the exponents in the prime factorization of 21#36?