Floor Plus Floor is Floor

Number Theory Level 5

$\left \lfloor \frac {n}{4} \right \rfloor + \left \lfloor \frac {2n+3}{7} \right \rfloor = \left \lfloor \frac {8n+9}{15} \right \rfloor$

Find the largest natural number that satisfy the equation above.

(This problem is from the OMA)

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