What is the expiation required from someone who swore by Allah inadvertently (laghw), or broke an oath, and does not remember the number of times?

Perpetuating excessive swearing is blameworthy in Islamic law, as Allah Almighty says: ﴿And do not make [your oath by] Allah an excuse against being righteous﴾ (Al-Baqarah: 224), and His saying: ﴿And do not obey every [habitual] swearer, contemptible﴾ (Al-Qalam: 10).

A vain oath (laghw al-yameen), which is what flows from the tongue unintentionally, entails nothing, as Allah Almighty says: ﴿Allah will not impose blame upon you for what is unintentional in your oaths﴾ (Al-Ma'idah: 89). If the oaths are of this type, then no expiation is due from you.

However, if the oaths were binding and you forgot their number, then you must offer expiation for the number of oaths of which you are certain, and nothing is due from you for what you doubt; because the default is the acquittal of one's liability. If you offer expiation for the doubted number as a precautionary measure, then that is good.