Apple ID verification without access to other devices.

I am reinstalling OS X (yosemite) on my 2011 Mac desktop after an erasure of the disk. When I am entering my Apple ID I am getting the following message:

"An Apple ID verification code is required to sign-in. Type your password followed by the verification code shown on your other devices."

The issue with this being that both my other devices, an iPhone 5s and an iPad are either smashed or not fully operating, so it is seemingly not possible to get that verification code from them.

What can I do to verify and reinstall and begin to use my Mac again?

Many thanks in advance,

Henry