Number Inception

I am thinking of a number that is 10 digits long. No figure is repeated (i.e. it uses ever digit in the range 0-9 once and only once).

The first digit is divisible by 1.

The number contrived by the first two digits divides exactly by 2.

The number contrived by the first three digits divides exactly by 3.

The number contrived by the first four digits divides exactly by 4.

The number contrived by the first five digits divides exactly by 5.

The number contrived by the first six digits divides exactly by 6.

The number contrived by the first seven digits divides exactly by 7.

The number contrived by the first eight digits divides exactly by 8.

The number contrived by the first nine digits divides exactly by 9.

The number contrived by the all ten digits divides exactly by 10.

What is my number?

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