Synodic months are just over 29 days long. Most ancient peoples relied on a lunisolar calendar if they went the lunar route, and noticed that the seasons cycled within 12 synodic months. This gives about 354 or so days in a year, given the unevenness with the lunar cycle.
So, even a lunar calendar doesn't fix it.
So, even a lunar calendar doesn't fix it.
"I was thirsty for everything, but blood wasn't my style" - Live, "Voodoo Lady"