Teaser 2950: Ten digits

From The Sunday Times, 7th April 2019 [link]

Without repeating a digit I have written down three numbers, all greater than one. Each number contains a different number of digits. If I also write down the product of all three numbers, then the total number of digits I have used is ten. The product contains two pairs of different digits, neither of which appear in the three original numbers.

What is the product?