What least number can be multiplied by 165375 to make it a perfect cube?

To find the least number that should be multiplied by 165375 to make it a perfect cube, we first find the prime factorization of 165375.
Let's divide 165375 by its prime factors:

165375÷5=33075

33075÷5=6615

6615÷5=1323

1323÷3=441

441÷3=147

147÷3=49

49÷7=7

7÷7=1

So, the prime factorization of 165375 is:

165375=3
3
×5
3
×7
2

For a number to be a perfect cube, the power of each prime factor in its prime factorization must be a multiple of 3.

The power of 3 is 3 (already a perfect cube).

The power of 5 is 3 (already a perfect cube).

The power of 7 is 2. To make it a perfect cube, it needs to be multiplied by 7
1
.

Therefore, the least number to be multiplied is 7.