Which is the greatest 6-digit number divisible by 4, 8, 10, 6, 9, 15, 45, 24, 36 and 20?

The answer is 999720.

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When a number $N$ is divisible by $4, 6, 8, 9, 10, 15, 20, 24, 36,$ and $45$ means that $N$ is divisible by the lowest common multiple of $4, 6, 8, 9, 10, 15, 20, 24, 36,$ and $45$ . And $\text{lcm }(4, 6, 8, 9, 10, 15, 20, 24, 36, 45) = 2^3 \times 3^2 \times 5 = 360$ .

The greatest 6-digit divisible by $360$ is $\left \lfloor \dfrac {1000000}{360} \right \rfloor \times 360 = 2777 \times 360 = \boxed{999720}$ .

Notation:$\lfloor \cdot \rfloor$ denotes the floor function .