How to solve a cryptarithm?

Question

Given multiplication is $$\begin{array}{cccccc} & & & P & E & N \\ & & & I & N & K \\\hline & & L & K & P & R \\ & I & R & T & N & \\ E & A & K & N & & \\\hline L & E & T & T & E & R \end{array}$$

how to find the values of the letters?

Answer 1

Start from N*N ends in N, so N must be 5 or 6 (can't be 0 or 1 from the second line in the sum). Then I*N ends in N (and I !=1) says N is 5 and I is odd. Then K is even and R is 0. Continue

Answer 2

6 1 5 * 354

 2 4 6 0

3 0 7 5

1 8 4 5

2 1 7 7 1 0