The product of 45 and 15 is \( 45 \times 15 = 675 \).
Since 675 is a whole number, it is classified as:
- an integer
- rational (since all integers are also rational numbers, as they can be expressed as the quotient of an integer and 1)
However, in the context of the closure property for the product of two numbers, the most direct answer to the question is that it is:
an integer.