$2016$ is unique number because of its consecutive divisors from $1-9$. Find the next whole number with the same property

Question

$2016$ is unique number because of its divisors (1,2,3,4,6,7,8,9). Find the next whole number with the same property!

First, I know that $2016$ have $36$ divisors: $$1, 2, 3, 4,6,7,8,9,12,14,16,18,21,24,28,32,42,48,56,63,72,84,96,112,126,144,168,224,252,288,336,504,672,1008,2016$$ With a prime factorization of: $$2^5 \times 3^2 \times 7$$

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How do I continue? Hints Only.

Answer 1

A number is divisible by $2,3,4,6,7,8,9$ if and only if it is a multiple of $$lcm(2,3,4,6,7,8,9)=504$$ After $2016$, the next number is $2520$