During sandhyavandhanam.. how many times we need to chant the gayathri mantra...how much is the minimum number..
Gayathri is called Vedha Matha- the mother of Vedhas. And Gayathri Japa is a duty of every Dwija. (Dwija is not only a Brahmin but includes even Kshatriyas and Vaishyas - who are initiated with Brahmopadesha and given Upanayanam.
It is one of the foremost duty given to you... Consider the case of your employment... You are given the promised salary for the work you do and do not get any additional or special pay for doing your job.. but you are questioned or even punished when you fail to do it.. The same is the case with Sandhyavandhanam.. By doing it you dont gain any special punya. But by leaving it you incur papa.
Gayathri Japam is a part of Sandhya vandhanam. The significant feature of Sandhyavandanam is the self contemplation or meditation through the Gayatri Mantra.
This is done first and foremost for one's personal Shreyas as well as Lokakshemam.
Simply chanting this Japa is of no use. One's mind should be completely focused towards Gayathri Devi. Minimum of 1008 times, is what our Shastras suggest. And if its not possible, it is suggested for a minimum of 108 times.
And now people need to reduce it even. Not only gayatri, any mantra - the more is the number the more you are benefited.
-------- An interesting episode is to be seen in an Islamic book "Akbar nama", the biography of Emperor Akbar
when Akbar was ruling India . Birbal was his minister .Akbar and Birbal would often travel incognito to collect first hand information about the various happenings within the country.
On one occasion , they noticed a brahmin going begging from house to house. Akbar pointed this out to Birbal. Birbal noticed the beggar and kept quiet. After reaching home he sent word for the brahmin to meet him.
When the brahmin called on Birbal , Birbal said ,
"Oh ! Brahmin - You collect your daily earnings through begging from me every day . In lieu of begging please chant Gayatri Japam during the three sandhya periods 108 times everyday. I shall pay you daily for chanting the mantra"
The brahmin agreed and after collecting the money from Birbal, started chanting Gayatri Mantra. This continued daily. After a few days , he thought , why not increase the chanting to 1008 times, since he had a lot of time. Birbal paid him more for increasing the count. This continued for some days but after few days the brahmin stopped going to Birbal's house for begging .
After a few days, Birbal suddenly remembered this Brahim and thought of inquiring about him. He visited the brahmin and asked him as to why he had stopped coming to his house. He was really surprised to see more and more people visiting the brahmin for his blessings and he had become a well known personality. The brahmin welcomed Birbal and profusely thanked him for putting him on the right path by guiding him at the right time. His daily meditation earnt him the power to acquire knowledge , acquire an attractive personality and soon he transformed into a good expounder of knowledge.
One day Birbal mentioned to Akbar that a saintly person had come to town and Akbar promptly invited the person and honoured him. Birbal then asked Akbar whether he remembered this saintly person but akbar could not recollect. Birbal then reminded Akbar about the brahmin beggar episode . Akbar after hearing this exclaimed "Oh! what a change".
This episode appears in the Akbar Nama and brings out the virtue and greatness of the Gayatri Mantra.
Coming to your question, the minimum in 108.. But Shastras say during Aapath-kaalam(when one is in danger or extraordinary situation) one can chant a minimum of 10 gayathri. If you chant Gayatri for 10 times in a fully involved manner, she will definitely going to bless you. But you have to decide whether are you always in Aapath Kalam? By doing Gayathri Japa, a dwija will grow and glow in social and spiritual life and reach the final destiny.