Determine the multiplying and the multiplier

Question

In the product below, $“*”$ replaces digits other than $“3”$ and not necessarily the same. Determine the multiplying and the multiplier.

I couldn't do much but find out that the number of units in the first is $7$ and the number of tens in the second is $9$.

Edit: In the solution I saw, it says that the hundreds of the second digit being $7 $ is not acceptable. why?  

Answer 1

The thousands digit of the multiplicand must be $1$ so that the first digit of the first product is $3$.

The hundreds digit of the multiplicand must be $1$ or $2$ so as not to carry and spoil the $3$.

To get five digits for the second line when the multiplicand is no greater than $1239$ the tens digit of the multiplier must be $9$ and the ones digit of the multiplicand must be $7$, so we have either $1237 \times *93$ or $1137 \times *93$

The greater of these gives a product without the hundreds of the multiplier of $1237\cdot 93=115,041$. The hundreds digit of the multiplier has to be large enough to carry into the millions and $7$ is not enough, so the multiplier is $893$.

We get $1137 \times 893 =1,015,341$, but that is not acceptable because of the $3$. The other choice is $1237 \times 893=1,104,641$