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

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