Find the smallest number by which 675 must be multiplied to obtain a perfect cube.

675 = 3 x 3 x 3 x 5 x 5

Here, we can see that two 5s are left which are not forming a triplet. To make 675 a cube, one more 5 is needed

Hence,

675 x 5 = 3 x 3 x 3 x 5 x 5 x 5 = 3375

We know that 3375 is a perfect cube.

Therefore, the smallest natural number by which 675 should be multiplied to make it a perfect cube is 5.