Find the smallest positive integer 'k' such that 360k is a cube number. Can somebody please explain how to do this?

Question

hartnn · Answer

a cube number is of the form, x*x*x 

can you factorize 360 ?

anonymous · Answer

36*10 = 2*2*3*3*2*5 and you'll need 3 of each...

anonymous · Answer

360k = (180)(2)k = (90)(2)(2)k = (45)(2)(2)(2)k = (15)(3)(2)(2)(2)k = (5)(3)(3)(2)(2)(2)k
and now you can see what do you need to have a perfect cube:
if you have $$(5)^{1} (3)^{2} (2)^{3} (k)$$ ... then?

anonymous · Answer

Thank you

anonymous · Answer

did you find k?  if so, share please

anonymous · Answer

not quite...
360 = 2*2*2*3*3*5  so you need to multiply by 3*5*5 = k in order to make the smallest perfect cube.  make sense?  you need 3 of each and you already have three 2's but only two 3's and one 5.