Dimensions of the Cuboid:
Length = 15 cm
Breadth = 6 m
Height = 9 dm

To find the volume, lateral surface area, and total surface area of the cuboid, we will follow the given dimensions and use the formulas for each calculation.

Volume of the Cuboid:
The volume of a cuboid is given by the formula:
Volume = Length x Breadth x Height

Given:
Length = 15 cm
Breadth = 6 m (1 m = 100 cm, so 6 m = 6 x 100 = 600 cm)
Height = 9 dm (1 dm = 10 cm, so 9 dm = 9 x 10 = 90 cm)

Substituting the values into the formula:
Volume = 15 cm x 600 cm x 90 cm
= 810,000 cm³

Hence, the volume of the cuboid is 810,000 cm³.

Lateral Surface Area of the Cuboid:
The lateral surface area of a cuboid is the sum of the areas of its four vertical faces.

Given:
Length = 15 cm
Breadth = 6 m (600 cm)
Height = 9 dm (90 cm)

The lateral surface area can be calculated as follows:
Lateral Surface Area = 2 x (Length x Height) + 2 x (Breadth x Height)

Substituting the values into the formula:
Lateral Surface Area = 2 x (15 cm x 90 cm) + 2 x (600 cm x 90 cm)
= 2 x 1350 cm² + 2 x 54000 cm²
= 2700 cm² + 108000 cm²
= 110700 cm²

Hence, the lateral surface area of the cuboid is 110700 cm².

Total Surface Area of the Cuboid:
The total surface area of a cuboid is the sum of the areas of all its six faces.

Given:
Length = 15 cm
Breadth = 6 m (600 cm)
Height = 9 dm (90 cm)

The total surface area can be calculated as follows:
Total Surface Area = 2 x (Length x Breadth) + 2 x (Length x Height) + 2 x (Breadth x Height)

Substituting the values into the formula:
Total Surface Area = 2 x (15 cm x 600 cm) + 2 x (15 cm x 90 cm) + 2 x (600 cm x 90 cm)
= 2 x 9000 cm² + 2 x 1350 cm² + 2 x 54000 cm²
= 18000 cm² + 2700 cm² + 108000 cm²
= 127,700 cm²

Hence, the total surface area of the cuboid is 127,700 cm².

In summary:
- The volume of the cuboid is 810,000 cm³.
- The lateral surface area of the cuboid is 110700 cm².
- The total surface area of the cuboid is 127700 cm².