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I left mine on when I applied. Honestly, I didn't really think about it as an issue since if I got hired I'd have to give up my social anyway. I'm not sure what harm someone could do with your LSAC number. I did apply to only one company that was very reputable, so your comfort will probably vary based on the rep of the company.

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While you do have to report them your SSID# if you actually got the job, I see no reason not to be prudent and white it out. May as well white out your LSAC# but I don't think much harm can come from people knowing that one.

White out your name while you're at it. Don't let them have too much information.

All kidding aside, yeah it's probably OK to redact either one. I think rather than whiteout though, I'd use orange or green highlighter (whichever one photocopies as black) prior to scanning.