In reply to tistimetogo:
I've done quite a lot of this over the years, so have kept records to make estimating easier. My average would suggest you'll need about 45-50 regular sized (i.e. 190-220g) cylinders. This is for medium altitude use with no melting of snow. If you're melting snow for everything you'll be close to doubling that requirement, but that seems unlikely at 3700m in summer.
Other factors to take into account include how sheltered from the wind your cooking set-up will be, what kind of food you are cooking, the temperature of the water you're starting with, etc. Using a few black Ortlieb water storage bags placed in the sun to boost the water temperature during the day can make a big difference to cooking/boiling times. The figure above is for using a well windshielded stove in the porch of a tent and eating a mix of freeze dried and more regular food (e.g. tins of stew and tatties, pasta and sauce).
John