Step 1: Convert all units to centimeters

Since the brick dimensions are given in centimeters ($24\text{ cm} \times 12\text{ cm} \times 8\text{ cm}$), convert the wall dimensions from meters to centimeters: Length = $24\text{ m} = 2400\text{ cm}$, Height = $8\text{ m} = 800\text{ cm}$, Thickness = $60\text{ cm}$.

$\text{Length} = 2400\text{ cm}, \text{Height} = 800\text{ cm}, \text{Thickness} = 60\text{ cm}$

Step 2: Calculate total volume of the wall

Multiply the length, height, and thickness of the wall to find its total volume.

$V_{\text{wall}} = 2400 \times 800 \times 60 = 115,200,000\text{ cm}^3$

Step 3: Account for mortar volume

Since $10\%$ of the wall is filled with mortar, the volume occupied by bricks is $90\%$ of the total wall volume.

$V_{\text{bricks}} = 0.90 \times 115,200,000 = 103,680,000\text{ cm}^3$

Step 4: Calculate volume of a single brick

Find the volume of one brick using its given dimensions.

$V_{\text{1 brick}} = 24 \times 12 \times 8 = 2304\text{ cm}^3$

Step 5: Calculate the required number of bricks

Divide the total volume occupied by bricks by the volume of one brick to find the total number of bricks.

$N = \frac{103,680,000}{2304} = 45,000$