Assalaamu alaykum wa rahmatullaahi wa barakaatuhu. I was told that reciting Surah Al-Iklaas [Quran 112] thrice is equal to reading the whole Quran. Should one recite the Basmalah (saying Bismillaahi Ar-Rahmaani Ar-Raheem [in the name of Allah, the Most-Merciful, the Ever-Merciful]) each time for that, or is reciting it once enough? Kindly clarify.

All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger.

If you wish to repeat Soorah Al-Ikhlaas or other Soorahs, you should repeat the Basmalah each time you start one. Ibn Al-Jazari wrote, "I could not find a text regarding the case when the last verse of a Soorah is recited and followed directly with the opening verse of the same Soorah, when repeating Soorah Al-Ikhlaas, for example, without a pause. The most likely correct view is that the Basmalah must be recited, because the Soorah is recited from the beginning." [An-Nashr]

Allah knows best.