# Lcm Gcd

Number Theory Level pending

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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