Why do mantras usually end with Shantih Shantih Shantih (3 times)?

Question

At the end of most of Mantras from Vedas & Upanishads, we find Om Shanti Shanti Shanti. As in the end of this Mantra,

ॐ असतो मा सद्गमय ।
तमसो मा ज्योतिर्गमय ।
मृत्योर्मा अमृतं गमय ।
ॐ शान्तिः शान्तिः शान्तिः ॥
Om Asato Maa Sad-Gamaya |
Tamaso Maa Jyotir-Gamaya |
Mrtyor-Maa Amrtam Gamaya |
Om Shaantih Shaantih Shaantih ||

Meaning:
1: Om, Lead us from Unreality (of Transitory Existence) to the Reality (of the Eternal Self),
2: Lead us from the Darkness (of Ignorance) to the Light (of Spiritual Knowledge),
3: Lead us from the Fear of Death to the Knowledge of Immortality.
4: Om Peace, Peace, Peace.

As I want to know,

• What is the purpose of adding om shanti shanti shanti at the end of most mantras?
• What is the meaning of om shanti shanti shanti ?
• Why does it written Only for three times? Why not more or less than three times?

Answer 1

In his commentary on Taittirīya Upaniṣad, Śaṅkarācārya explains as follows.

ॐ शान्तिः शान्तिः शान्तिः ॥ ३ ॥

oṃ śāntiḥ śāntiḥ śāntiḥ || 3 ||

3. Om! Peace! Peace! Peace!

The uttering of the word ‘peace’ three times is intended to ward off the troubles that occur on the path to wisdom owing to causes operating in the individual organism, in the external beings, and in the region of Devas or Cosmic Intelligences.

Having thus prayed to the perceptible Brahman as Vāyu, the student contemplates by means of Praṇava which designates Him—the imperceptible Antaryāmin, the Ruler within, and prays for the removal of obstacles:

There are three kinds of troubles:

1. the Ādhyātmika, those which arise from causes operating in the student’s own body, namely, fever, pain in the head, and so on;

2. the Ādhidaivika the troubles from the Devas etc.;

3. the Ādhibhautika, troubles arising from Yakṣas, Rākṣasas, etc.

For the cessation of these three, the word 'peace' is uttered thrice. That the contemplation of Īśvara by Praṇava is meant for the removal of obstacles is formulated by Patañjali in four Sūtras as follows:

"Īśvara is a particular soul untouched by affliction, works, fruition and impressions. His designation is Praṇava. A constant repetition of it and an intense meditation on its meaning should be practised. Thence arises a cognition of the Inner Consciousness and absence of obstacles."

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By the way, the asato mā sadgamaya mantra you cite in your question is actually part of The Bṛhadāraṇyaka Upaniṣad (1.13.28) and neither does it begin with an ॐ (Oṃ) nor does it end with Oṃ Śāntiḥ Śāntiḥ Śāntiḥ.

Answer 2

It is repeated three times to bring safety to the individual chanting it. It is for

1. safety from wild animals (tigers, bears, etc.),
2. safety from natural disasters (floods, earthquakes, etc.),
3. safety from diseases and other afflictions of the body.

Safety from these three allows a person to worship and meditate in peace.

Swami Nikhilananda says in his explanation of one of the Peace Chants from the Upanishads (the different chants that are done at the start and end of each Upanishad):

The word is thrice repeated in order to remove the three possible obstacles that both the teacher and the disciple may meet with, namely, physical illness, natural calamity, and injury from harmful animals. The Supreme Lord [OM] is invoked at the commencement and the termination of the study of the Vedas and other scriptures for the removal of all faults committed intentionally, unintentionally, carelessly, or through excitement, oversight, or non-observance of the proper rules.

The earliest reference to the three Duhkhas (for which shanti is chanted three times) is by Kapila in his Sankhya Aphorisms (I.1.) and are defined:

1. due to one's self (ádhyátmika),
2. due to products of the elements (ádhibhautika), and
3. due to supernatural causes (ádhidaivika)

Answer 3

In the English translation (translated by Mahadeva sastry) of commentary of Taittiriya Upanishad based on Shankaracharya, Sureshwara and Sayana the following is the reason provided for doing the "peace" chant thrice, during santhi matras –

The uttering of the word 'peace ' three times is intended to ward off the troubles that occur on the path to wisdom owing to causes operating in the individual organism, in the external beings, and in the region of Devas or Cosmic Intelligences.

The student who studies the vedas, contemplates by means of Praanava, on Antaryamin, the Ruler within the self, and prays for the removal of obstacles

There are three kinds of troubles:

1. the Adhyatmika, those which arise from causes operating in the student's own body, namely, fever, pain in the head, and so on

2. the adhidaivika the troubles from the Devas etc.

3. the Adhibhautika, troubles arising from Yakshas, Rakshasas,etc

For the cessation of these three kinds of troubles, the word ' peace' is uttered thrice.

(I, think, same meaning is provided by SriRangaRamanuja muni (16 th century) in his Upaanishad Bhasya as per Vishistadvaita. The same meaning is provided by Sri U Ve.Uruppattur Dr. Rajagopalachariar Swamin in his Taittiriya upanishad upanyasam, in tamil, which is available on you tube)