Comparing Information In Two Spreadsheets

I have two spreadsheets. Spreadsheet A has a column of numbers representing employee IDs (thousands of them). But I need to also have the First and Last Name for these employees to cross-reference. Spreadsheet B has the employee ID, Last Name, First Name. Spreadsheet A is large and grouped in a way that I cannot just sort by the employee ID to match up with Spreadsheet B. So basically what I am trying to do:

Look in Spreadsheet B for the employee ID found in Spreadsheet A. If found insert the information in the Last Name and First Name cell for that row copied into Spreadsheet A

Example:Spreadsheet A
Employee ID
123456
412378
<blank cell>
512345
685217
654553

Spreadsheet B
123456 Alberts Rick
654553 Johnson Mark
412378 Smith John

So I want for Spreadsheet A to compare with Spreadsheet B. If 123456 is found in Spreadsheet B, then put Alberts and Rick in the corresponding cells next to 123456 in Spreadsheet A.