Let \(\overline{739ABC} \) be a 6-digit number that is divisible by 7, 8 and 9. Denote \(M\) and \(N\) as two possible lowest common multiple of the three integers, \(A,B\) and \(C\), such that \(P = \gcd(M,N) \). Find \[ \sqrt{\dfrac{M+N}{P^{2/3} } } . \]

If you think that it is impossible to have two lowest common multiples, submit your answer as 3.142.

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