Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube.(i) 243                   (ii) 256            (iii) 72               (iv) 675(v) 100

Explanation

To find the smallest number by which each of the given numbers must be multiplied to obtain a perfect cube, we will follow these steps for each number:

### (i) For 243:
1. **Prime Factorization**:
- 243 = 3 × 3 × 3 × 3 × 3 = \(3^5\).
2. **Grouping Factors**:
- We can group the factors into triplets: \(3^3\) (one triplet) and \(3^2\) (a pair).
3. **Finding the Missing Factor**:
...