Solve Three-Digit Addition: 157 + 264 in Vertical Format

$\begin{aligned} &157 \\ +& \\ &264 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

To solve this problem, we'll perform vertical addition:

• Write the numbers 157 and 264 in a column, aligning the digits by place value. Start from right (units) to left (hundreds).
• Step 1: Add the digits in the units place $7 + 4 = 11$. Write down 1 and carry over 1 to the tens column.
• Step 2: Add the digits in the tens place $5 + 6 = 11$, plus the carried 1 from the previous step, giving a total of 12. Write down 2 and carry over 1 to the hundreds column.
• Step 3: Add the digits in the hundreds place $1 + 2 = 3$, plus the carried 1 from the previous step, resulting in 4. Write down 4.

After adding each column and managing the carries appropriately, the resulting sum of these numbers is 421.

Therefore, the solution to the problem is $421$.