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

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#### Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.