Find the smallest positive integer N that satisfies all of the following conditions:

• N is a square.

• N is a cube.

• N is an odd number.

• N is divisible by twelve prime numbers.

How many digits does this number N have?

Hey 👋

to be odd, it cannot have 2 as a factor.

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In step by step.

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I understand your approach; thanks

12/3/2008

Birth of date

Of course, good checkup oobleck.

are you sure, you answerd all the points of it.

Please anser my question. Urgent!

If any one can solve; please do and share the answer in step by step.

obviously we have to take out the factor of 2 since multiplying anything

by 2 would make it even, so

3*5*7*11*13*17*19*23*29*31*37

Please answer the question in detail.

In step by step.

Answer full, not hints.

Please Answer ASAP

The trouble is the divisibility by the first 12 prime numbers,

so it must be a multiple of 2*3*5*7*11*13*17*19*23*29*31*37

To be odd it must look like 2K+1

to be a square it must look like (2K+1)^2, and it must also be a cube
it must contain (2K+1)^6

so, it must have the form:
2*3*5*7*11*13*17*19*23*29*31*37(2K+1)^6
when K = 0, we get
2*3*5*7*11*13*17*19*23*29*31*37(1)^6
= 7.420738135... x 10^12
which would be 13 digits long