Two pieces of cloth measure 96 metres and 144 metres in length. What is the maximum length of cloth that can be cut equally from both pieces without any remainder?

Correct option is D

Concept used :

To find the maximum length of cloth that can be cut equally from both pieces without any remainder, we need to determine the Greatest Common Divisor (GCD) of the lengths of the two pieces of cloth (96 m and 144 m).

Solution :

Prime factorization of 96:

96 = $$2^5 \times 3$$​​

Prime factorization of 144:

144 = $$2^4 \times 3^2$$​​

Identify the common factors:

​$$\text{GCD} = 2^4 \times 3 = 16 \times 3 = 48$$​​

The maximum length of cloth that can be cut equally from both pieces is 48 metres.