This is more of a legal question but I agree with @Bsch4477
Your business can deduct ordinary and necessary expenses of running the business. Paying a nanny is a personal expense, not a business expense. So while you could maybe issue the checks in the name of the business and remit the employment taxes on the LLC's form 941, you can't deduct the nanny's salary as a business expense.
If it were me, I would keep things separate and pay the nanny from personal funds and report it on schedule H under your own SSN instead of the LLC EIN.
