Question

Find the smallest number that is multiple with 540 to make a perfect cube

Answer 1

Hey I got the answer...


When 540 is divided by 20 ,,,

Then, 540 ÷ 20 = 27

27 is a cube of 3

Therefore 20 is the smallest number that is multiple with 540 to make it a perfect cube.

Answer 2

Correct question:

What is the smallest integer which can you multiply to 540 to make it a perfect cube?

Answer:

The smallest integer which can you multiply to 540 to make it a perfect cube is 50.

Step-by-step explanation:

Given,

The number 540

To find,

The smallest integer which can you multiply to 540 to make it a perfect cube

Calculation,

We try to find out the prime factorization of 540:

I.e. 540 = 54×10 = 9×6×10 = 3 × 3 × 3 × 2 × 5 × 2  

⇒ 540 = 3³ × 2² × 5...(1)

Now to make the number a perfect cube we need to make all the power of the prime numbers as cubes.

i.e. We need to multiply the equation (1) by 2 × 5²

540 × 2 × 5² = 3³ × 2³ × 5³

⇒ 540 × 50 = 30³

Therefore, the smallest integer which can you multiply to 540 to make it a perfect cube is 50.

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