How many centroids do we need?

Geometry Level 3

Let \(P\) be any point inside a triangle \(ABC\). We further denote
- \(L\) as the centroid of the triangle \(PBC\).
- \(M\) as the centroid of the triangle \(PAC\).
- \(N\) as the centroid of the triangle \(PAB\).

What is the ratio of area of triangle \(ABC\) to the area of triangle \(LMN\)?

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