\[\large\overline{aaaaaa}=\overline{bc} \times b c (2c-b) (2b+c) ( c-b) \]

If natural numbers \(a,b,c\) satisfy the above equation , find the product \(abc\) .

**Details And Assumptions:**

- \(\overline{bc}\) is a two digit number and \(\overline{aaaaaa}\) is a six digit number.

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