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Changing a number to a Perfect Cube

Changing a number to a Perfect Cube

Secondary 1
  1. Find the smallest possible positive integer \(k\) such that \(7920k\) is a cube number.
  2. Find the smallest possible positive integer \(k\) such that \(8400k\) is a cube number.
  3. What is the greatest perfect cube that is a factor of \(124416\)?
  4. Find the smallest positive integer value of \(n\) such that \(800n\) is both a perfect square and a perfect cube.

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Answer:(i) 36300; (ii) 8820; (iii) 13824; (iv) 1250.

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