Remainder in AP?

Number Theory Level pending

Rahul decides to open his father's laptop. But it is password protected. His father being a mathematician has left a mathematical hint for the password. It had the following contents:

Password is a natural number and it is the least number satisfying the conditions given below.

  • The number when divided by 2 leaves remainder 0
  • The number when divided by 3 leaves remainder 1
  • The number when divided by 4 leaves remainder 2
  • The number when divided by 5 leaves remainder 3
  • The number when divided by 6 leaves remainder 4
  • The number when divided by 7 leaves remainder 5
  • The number when divided by 8 leaves remainder 6
  • The number when divided by 9 leaves remainder 7
  • The number when divided by 10 leaves remainder 8

Find the password.

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