The apparent meaning of the ahadith narrated from Sayyiduna Zayd bin Khalid al-Juhani and Sayyiduna Abdullah bin Amr (may Allah be pleased with them both) from the Prophet (peace and blessings be upon him) indicates that, in the matter of announcing it, there is no difference between a small and a large amount of lost property (luqatah) (both are equal).
Hadith Referenceالسنن الكبرى للبيهقي / كتاب اللقطة / Q12096
It is narrated from Sayyiduna Anas bin Malik (may Allah be pleased with him) that the Messenger of Allah (peace and blessings be upon him) passed by a date.
He (peace and blessings be upon him) said: "Were it not that it might be from the charity, I would have eaten it."
Hadith Referenceالسنن الكبرى للبيهقي / كتاب اللقطة / 12096
It is narrated from Sayyiduna Anas (may Allah be pleased with him) that the Messenger of Allah (peace and blessings be upon him) passed by a date lying on the road, and he (peace and blessings be upon him) said: "Were it not that I fear it may be from the charity, I would have eaten it."
Hadith Referenceالسنن الكبرى للبيهقي / كتاب اللقطة / 12097
It is narrated from Sayyiduna Jabir bin Abdullah (may Allah be pleased with them both) that the Messenger of Allah (peace and blessings be upon him) permitted us to pick up a stick, a whip, a rope and similar things: "A man may pick them up and make use of them."
Hadith Referenceالسنن الكبرى للبيهقي / كتاب اللقطة / 12098
It is narrated from Sayyiduna Jabir (may Allah be pleased with him) that the Messenger of Allah (peace and blessings be upon him) granted us permission, and he did not mention the rope.
There is doubt about whether this hadith is marfu' (attributed to the Prophet), and there is weakness in its chain.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب اللقطة / 12099
It is narrated from Sayyiduna Ya'la bin Murrah (may Allah be pleased with him) that the Messenger of Allah (peace and blessings be upon him) said: "Whoever finds a small lost item, a rope, a dirham or something similar, let him announce it for three days; and if it is more than that, let him announce it for six days."
Only Umar bin Abdullah bin Ya'la narrated it; Yahya bin Ma'in declared him da'if (weak), and Jarir bin Abd al-Hamid and others accused him of drinking wine.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب اللقطة / 12100
Abdullah bin Farrukh, the freed slave of Talhah, said: I heard Sayyidah Umm Salamah (may Allah be pleased with her) being asked about picking up a whip. She said: If one picks up his brother's whip and makes use of it, I see no harm in it. He said: And a rope? She said: And a rope. He said: And sandals? She said: And sandals. He said: And a container? She said: I do not make lawful what Allah has forbidden; a container may hold money for spending, and it may hold goods.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب اللقطة / 12101