1. Break down the numbers using their place values:
13 = 10 + 3
27 = 20 + 7
2. Construct the multiplication grid (generic triangle method):
\begin{array}{c|c|c} & 20 & 7 \\\hline10 & 10 \times 20 & 10 \times 7 \\ & = 200 & = 70 \\\hline3 & 3 \times 20 & 3 \times 7 \\ & = 60 & = 21 \\\end{array}
3. Sum the individual products obtained in the grid:
200 + 70 + 60 + 21
4. Calculate the total sum:
200 + 70 = 270
270 + 60 = 330
330 + 21 = 351
Therefore, the final answer is:
351