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A 3 digit number is multiplied by a 2 digit number and the calculation is written out as shown below.
Each star like this stands for one digit.

Apart from the zero shown the only digits which occur are 2, 3, 5 and 7. This is sufficient information to complete the whole multiplication.

       

This is sufficient information to complete the whole multiplication sum.
       

You might find this sheet useful for working on the problem,