The Multiplication

Puzzle:

In the following multiplication, certain digits have been replaced with asterisks (*). Replace all the asterisks such that the problem holds the result.

.......* * 7
X.....3 * *
.....---------
......* 0 * 3
......* 1 *
...* 5 *
...------------
...* 7 * * 3

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Solution:

.......1 1 7
X.....3 1 9
.....---------
......1 0 5 3
......1 1 7
...3 5 1
...------------
...3 7 3 2 3