Can I use a 2009 13-inch MacBook Mac OS X Installation Disc to Repair the Disc in my 2006 13-inch MacBook?

I have a 13-inch MacBook (Model No. A1181) that was purchased in the summer of 2006 with Mac OS X 10.6 (Snow Leopard) on it. I have been trying to clean up this MacBook in an effort to get it to run more efficiently. First, I Verified and Repaired Disk Permissions using Disk Utility. That completed successfully.

Second, I tried to Verify Disk using Disk Utility. This process stopped before completion with an error. The error reads,

Disk Utility stopped verifying "Macintosh HD"

This disk needs to be repaired. Start up your computer with another disk (such as your Mac OS X installation disc), an then use Disk Utility to repair this disk.

I do not have the installation discs/DVDs that came with this MacBook (2006) anymore. However, my mom has the installation discs that came with her 13-inch MacBook, purchased 12/2009. Can I use the Mac OS X installation disc (10.6) that came with her MacBook (2009) in my earlier model MacBook (2006) to repair the disk (Macintosh HD)?

Are there any other solutions?

Thank you,

Colin