A login password for the computer is not the password used for your Apple ID. To change a forgotten or lost password:
Forgot Your Account Password
For Lion, Mountain Lion, or Mavericks
Boot to the Recovery HD:
Restart the computer and after the chime press and hold down the COMMAND and R keys until the menu screen appears. Alternatively, restart the computer and after the chime press and hold down the OPTION key until the boot manager screen appears. Select the Recovery HD and click on the downward pointing arrow button.
When the menubar appears select Terminal from the Utilities menu.
Enter resetpassword at the prompt and press RETURN. Follow
instructions in the dialog window that will appear.
Or see:
Reset a Mac OS X 10.7 Lion Password
OS X Mountain Lion- Reset a login password,
OS X Mavericks- Solve password problems,
OS X Lion- Apple ID can be used to reset your user account password.
For Snow Leopard and earlier with installer DVD
Mac OS X 10.6- If you forget your administrator password,
OS X- Changing or resetting an account password (Snow Leopard and earlier).
For Snow Leopard and earlier without installer DVD
How to reset your Mac OS X password without an installer disc | MacYourself
Reset OS X Password Without an OS X CD — Tech News and Analysis
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