There is no such number. If someone claimed that x was such a number then x+2 would be (a) a greater number and (b) a product of 2. So then x could not be such a number.
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Since the greatest digit is 9 and the greatest 2-digit number is 99, the product of them is 891.
You will get the greatest product if you choose the greatest possible numbers in both cases, i.e., 9 x 99.
2 digit number
Their least common denominator is their product. Their greatest common denominator is infinite.
It is 891.