Two positive integers between 51 and 999 are both rounded to the nearest hundred. If these two numbers are multiplied together, which of the following must be true?

F
The product is less than 1000.

G
The product has a zero only in the ones and tens places.

H
The product has a digit greater than zero in the thousands place.

J
The product has a zero in the ones, tens, and hundreds places.

K
The product has a digit greater than zero in the ten-thousands place.