Can't find any numbers nationwide for that (though I didn't search too hard) but I did find estimates that there were ~700 prohibition related gang deaths in Chicago over the 13 years of prohibition, and ~1,000 in NYC. I'm going to assume that the vast majority of gang-related prohibition deaths were in major cities. There was an overall increase in the US murder rate by ~2.5 per 100k over the course of Prohibition, but that can't be exclusively attributed to Prohibition since the murder rate has already been rising steadily since 1904, and even though it dropped after 1933 we have the economic effects of the Great Depression as a major confounder.
Chicago had a population of 2.7 million in the 1920 census and 3.3 million in the 1930 census. NYC had a population of 5.6 million in the 1920 census and 6.9 million in the 1930 census.
Even if we use the lower 1920 numbers, that works out to ~2 Prohibition gang related murders per 100k population in Chicago per year. For NYC it's ~1.4.
Cirrhosis deaths during Prohibition ranged from 7.1 to 7.5 per 100k for the US as a whole. The study I linked attributes only 10-20% of the reduction to Prohibition, but other studies attribute more than that. The pre-Prohibition peak of 14.8 per 100k in 1907. It's likely that the temperance movement generally (which is what led to Prohibition) as well as state-level Prohibition acts prior to constitutional prohibition, contributed to this decline.
In any case, if we assume only 10% of the reduction was due to Prohibition, and we use the lowest of the Prohibition era cirrhosis numbers (7.1 per 10k), that works out to ~.7 per 100k fewer deaths per year due to alcoholism nationwide, as opposed to the gang murders focuses in cities (or about 13k total for the 1920 us population, or about 14k for the 1933 US population). If we assume 20% those numbers double, obviously, and if we attribute any more of the drop from the 1907 peak to state level prohibition movements, we have an upper bound of ~156k, though that's unlikely since cultural forces like the temperance movement probably played a significant role there as well.
There are plenty of arguments that can be made in favor of or against prohibition, but the most common arguments that I see ("It didn't actually reduce drinking!" and "Gang related killings outweigh the lives saved!") don't really hold water.
