# Positive integer and factor

• Nov 30th 2012, 03:42 PM
DiamondVH123
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
• Nov 30th 2012, 04:24 PM
abender
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 $\displaystyle (2\cdot3\cdot5)^6$.

This is how I would start the process of answering the problem. The language of the formal proof is the next step.
• Nov 30th 2012, 04:28 PM
Plato
Re: Positive integer and factor
Quote:

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 $\displaystyle 2^6$ the smallest multiple of two that is both a square and a a cube?
• Dec 4th 2012, 12:41 PM
DiamondVH123
Re: Positive integer and factor
Thanks i know how to answer it now