With the enlargement of wireless technology, Internet of Things (IoT) is emerging as a promising approach to realize smart cities and address lots of serious problems such as safety, convenience and efficiency. In order to avoid any possible rancorous attacks, employing lightweight cryptosystems is most effective to implement encryption/decryption, message authentication and digital signature for security of the IoT. LED is such a lightweight cipher with two flexible keysize variants in the IoT. Since its designing, a multitude of fault analysis techniques in chosen plaintext attacks focus on provoking faults on LED to derive the 64-bit and 128-bit secret keys. It is vital to investigate whether injecting faults allows breaking LED while the attackers have the weakest ciphertext-only attacking ability. This study presents ciphertext-only fault analysis with six different distinguishers on LED. The simulating experiments show that our analysis can recover its 64-bit and 128-bit secret keys with over 99 percent probability using the SEI, GF, GF-SEI, ML, HW and MAP distinguishers. The attack can not only improve the attacking efficiency, but also decrease the number of faults. The fault locations can be injected into the deeper round. It provides vital reference for security analysis of other lightweight ciphers in the IoT.