A good estimation would be about 600 men.
battalion alludes to the number of men therein. battalion commander alludes to the commander of the battalion
Via the Ho Chi Minh trail.
North Vietnam also drafted it's men; captured NVA pith helmets had graffiti written on them that read in Vietnamese, "Born in the North, died in the South."
1000
Some estimates say about 1 million men. This does not count the AAA (Anti-Aircraft Artillery) defending North Vietnam against US war planes, those were often manned by North Vietnamese women.
You'll not always get an accurate answer for those statistical questions, for example a Mechanized Infantry battalion in Vietnam was roughly 900 men, a tank battalion in Vietnam was about 570 men, and a straight leg outfit (regular infantry) averaged about 600 men (some sources will state 700 or 800 men). Airborne battalion's in Vietnam averaged about 600 men (or more) per battalion.
US Divisions varied in strength based upon their type. For example a US Army mechanized infantry battalion might consist of about 900 to 1000 men, whereas a straight leg battalion (straight infantry-no tracks (armored vehicles) might consist of about 600 men. A US Army armor battalion (tank battalion) will have a little less than 500 men. Two or more battalions to a brigade, two or more brigades equal a division. An more often than not, those US outfits were usually understrength, from sick-calls, AWOLS, DEROS, ETS, wounded, killed, etc. NVA divisions may have been comparable in strength to US divisions, as the NVA also obtained their men through conscription.
The Mormon Battalion brought a few women along as laundresses and cooks. Many of these women were the wives of men in the battalion.
Both the Communists (North Vietnam and the South Vietnamese Communists, known as the Viet Cong-VC) and the South Vietnamese governments "DRAFTED" their men. When we entered a village (town) and there were NO military age males around, we knew they were either, deceased, hiding, or serving in the North or South Vietnamese military.
Roughly 700 men.
IF you mean battalion...500-1000
The 39th Battalion was a regiment in the Australian Army. The group fought in both World Wars and by the time it was disbanded had, had 1666 men serve in it. There were only 32 men to survive the 39th Battalion, seven officers and 25 others.