The employer must pay the prevailing wage for each location and does need a LCA for each location. The employer may pay higher than the prevailing wage.
Attorney Robert Brown's (former INS Director, 1972-99) reply to your question is general in nature, and does not constitute legal advice as all facts are known to him. For specific advice or representation you should retain an attorney experienced in immigration law. Mr. Brown's reply on AVVO does not create an attorney/client relationship not constitute legal advice.
Under DOL regulations, the employer must pay 100% or higher of the prevailing wage for an H-1B employee. The employer is required to file a new LCA for each location where the H-1B employee will work. Please consult an immigration attorney to discuss this further.
Disclaimer: The information provided here is generalized and should not be relied upon as legal advice. This communication does not create an attorney-client relationship.