It is often said that there are 18 smritis. But despite searching for a long time I have not come across a single Hindu text that lists 18 smritis.
The Yajnavalkha smriti lists 20 smritis which I have listed below (although the number is sometimes reduced to 19 by considering the Likhita and Sankha smritis as one since the authors were brothers).
Manu, Atri, Vishnu, Harita, Yajnavalkya, Usana, Angira, Yama, Apastamba, Samvarta, Katyayana, Brihaspati, Parashara, Vyasa, Sankha, Likhita, Daksha, Gautama, Satatapa and Vashishta.
The Parashara Smriti also lists 20 smritis although it replaces Yama, Brihaspati and Vyasa with Kashyapa, Gargya and Pracheta. And the Padma Purana lists 36 smritis; its list is similar to the one used by Yajnavalkha but it omits Atri and adds the following 17 new smritis
Marichi, Pulastya, Pracheta, Bhrigu, Narada, Kashyapa, Vishvamitra, Devala, Rishyasringa, Gargya, Baudhayana, Paithinashi, Javali, Samantu, Paraskara, Lokaksh and Kuthumi
The only source I know which lists 18 smritis is the Divine Life Society of Swami Sivananda. But Sivananda does not mention his source nor did he belong to a well recognised monk order like the one at Sringeri Sarada Peetham or Kanchi Kamakshi Peetham so I don't think his list can be taken with a massive grain of salt.
