By what least number should 324 be multiplied to get a perfect cube?
From the prime factorization of 324 we get,
2 | 324 |
2 | 162 |
3 | 81 |
3 | 27 |
3 | 9 |
3 | 3 |
1 |
= 324 = 2 × 2 × 3 × 3 × 3 × 3 = 3 × 3 × 3 × 2 × 2 × 3
So to make it a perfect cube we must complete the triplet pairs of 2’s and 3’s.
Hence, it will be multiplied by 2 × 3 × 3 = 18.