1. The problem is to multiply 51 by 41 using vertical multiplication. 2. Write the numbers vertically: \begin{array}{r} 51 \\ \times 41 \end{array} 3. Multiply the units digit of the bottom number (1) by the top number (51): $$51 \times 1 = 51$$ 4. Multiply the tens digit of the bottom number (4, which is 40) by the top number (51): $$51 \times 4 = 204$$ Since this is actually 40, multiply by 10: $$204 \times 10 = 2040$$ 5. Add the two results: $$\cancel{51} + 2040 = 2091$$ 6. Therefore, the product of 51 and 41 is: $$\boxed{2091}$$