Lightweight Wallets Communication with Blockchain I understand how the Bitcoin core wallet communicates with the blockchain, but how do the lightweight wallets like Multibits, Electrum, etc, communicate with the blockchain?
You should have a look at the SPV (https://en.bitcoin.it/wiki/Thin_Client_Security#Simplified_Payment_Verification_.28SPV.29_Clients).

It was also mentioned by Satoshi in his paper at page 5 point 8:
https://bitcoin.org/bitcoin.pdf