Question

Find the smallest natural number by which 1200 should be multiplied so that the product obtained is a perfect cube

Answer 1

By prime factorisation:

1200=2*2*2*2*3*5*5

Divide both by 2 to make the 2 thrice on R.H.S

600=2*2*2*3*5*5

Multiply 3*3*5 so that they can come thrice

27000=2*2*2*3*3*3*5*5*5

27000=2*3*5

27000 is cube root of 30

So the smallest that it should be multiplied is 45