Box Problem Redux

Number Theory Level 5

\[a \times b \times c + d \times e \times f = g \times h \times i \]

Find largest 9 consecutive integers that can be arranged such that they satisfy the equation above.

What is the value of \(g \times h \times i\)?

That is, sum of the volumes of two boxes equals that of the third box. What is the volume of the third box?

Note: The integers \(a, b, c,\ldots, i\) are not necessarily in order. Only that 9 consecutive integers are used, each once.

Full credit for this wonderful problem goes to Vikram Pandya.

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