HELP with some probably very basic stuff

[matematicar]

Hey everybody,

I'm currently working on some number theory exercises and I'm stuck at some of those. Here is one: Determine the smallest positive integer that is divisible by 2, 3 and 5, and that is also both a perfect square and a perfect cube.

I didn't do much so far. I know that the smallest positive integer that is divisible by 2, 3 and 5 is 2x3x5=30 and if it is a perfect square it would be 30x30=900 but that is not a perfect cube.

Also if I build a perfect cube out of it, then it is not a perfect square.

I'm running in circle here. Can anybody help me with this one?

Thank you so much

 

[Deleted member 4993]

Hey everybody,

I'm currently working on some number theory exercises and I'm stuck at some of those. Here is one: Determine the smallest positive integer that is divisible by 2, 3 and 5, and that is also both a perfect square and a perfect cube.

I didn't do much so far. I know that the smallest positive integer that is divisible by 2, 3 and 5 is 2x3x5=30 and if it is a perfect square it would be 30x30=900 but that is not a perfect cube.

Also if I build a perfect cube out of it, then it is not a perfect square.

I'm running in circle here. Can anybody help me with this one?

Thank you so much

Note that all the numbers involved are primes.

 

[Steven G]

Hey everybody,

I'm currently working on some number theory exercises and I'm stuck at some of those. Here is one: Determine the smallest positive integer that is divisible by 2, 3 and 5, and that is also both a perfect square and a perfect cube.

I didn't do much so far. I know that the smallest positive integer that is divisible by 2, 3 and 5 is 2x3x5=30 and if it is a perfect square it would be 30x30=900 but that is not a perfect cube.

Also if I build a perfect cube out of it, then it is not a perfect square.

I'm running in circle here. Can anybody help me with this one?

Thank you so much

This might help. Note that x^6 = (x^2)^3 = (x^3)^2