What is the smallest number by which the following numbers must be multiplied, so that the products are perfect cubes ? (I)675              (ii) 1323                (iii) 2560

Explanation

To find the smallest number by which the given numbers must be multiplied to make them perfect cubes, we will perform the prime factorization of each number and analyze the factors.

### (i) For 675:

1. **Prime Factorization**:
- Divide 675 by 3:
\[
675 \div 3 = 225
...