Smallest number multiplied to get a perfect cube

Let’s do this by examples

Finds the smallest number multiplied to 1125 to get a perfect cube

We see that,

  1125  = 3 × 3 × 5 × 5 × 5

Since 3 does not occur triplets,

we multiply by 3 to make a triplet

So, our number becomes

  1125 × 3   = 3 × 3 × 5 × 5 × 5 × 3

                  = 3 × 3 × 3 × 5 × 5 × 5

Now, it becomes a perfect cube.

So, we multiply 1125 by 3 to make it a perfect cube

Finds the smallest number multiplied to 5324 to get a perfect cube.

We see that,

  5324 = 2 × 2 × 11 × 11 × 11

Here,

2 does not occur in triplets

So, we multiply by 2 to make triplet

So, our number becomes

    5324  × 2 = 2 × 2 × 11 × 11 × 11 × 2

    = 2 × 2 × 2 × 11 × 11 × 11

Now, it becomes a perfect cube.

So, we multiply 5324 by 2 to make it a perfect cube

Finds the smallest number multiplied to 968 to get a perfect cube.

We see that,

  968 = 2 × 2 × 2 × 11 × 11

Here,

11 does not occur in triplets

So, we multiply by 11 to make triplet

So, our number becomes

  968 × 11 = 2 × 2 × 2 × 11 × 11 × 11

Now, it becomes a perfect cube.

So, we multiply 968 by 11 to make it a perfect cube

Finds the smallest number divided to 400 to get a perfect cube.

We see that,

400  = 2 × 2 × 2 × 2 × 5 × 5

Here,

2 & 5 does not occur in triplets

So, we multiply by 2 × 2 × 5 to make triplet

So, our number becomes

  400 × 2 × 2 × 5 = 2 × 2 × 2 × 2 × 5 × 5 × 2 × 2 × 5

           = 2 × 2 × 2 × 2 × 2 × 2 × 5 × 5 × 5

Now, it becomes a perfect cube.

So, we multiply 400 by 2 × 2 × 5

i.e. 20  to make it a perfect cube