# Thread: Positive integer and factor

1. ## Positive integer and factor

Im stuck on this question:

What is the smallest positive integer that is divisible by the factor 2,3 and 5 and which is also square and a cube. Prove that this is the smallest such integer.

how would i start this?

thanks

2. ## Re: Positive integer and factor

In the prime factorization of a perfect square, the exponent of each factor must divide 2. Similarly, for a perfect cube, the exponent of each factor must divide 3. So, your answer is going to be $(2\cdot3\cdot5)^6$.

This is how I would start the process of answering the problem. The language of the formal proof is the next step.

3. ## Re: Positive integer and factor

Originally Posted by DiamondVH123
What is the smallest positive integer that is divisible by the factor 2,3 and 5 and which is also square and a cube. Prove that this is the smallest such integer.

Is $2^6$ the smallest multiple of two that is both a square and a a cube?

4. ## Re: Positive integer and factor

Thanks i know how to answer it now