Dishes Problem

I first started this problem by looking at the lowest common multiple of 2, 3, and 4, simply because the restrictions state that every 2 people have to share a dish, every 3 have to share, and every 4 have to share, thus the total number of dishes has to be a multiple of 2, 3, and 4.
The lowest common multiple is 12. With 12 people, and the restrictions on dishes, that makes 6 dishes of rice, 4 dishes of broth, and 3 dishes of meat. That totals to 13 dishes for every 12 people.
If I recognize that 65 is 13*5. That means 5 groups of 13 dishes, and subsequently, 5 groups of 12 people. Therefore, for 65 dishes, there must be 5*12 = 60 guests!

I don't believe cultural context has any effect on this problem. The fact that I'm working on this Chinese problem from the 4th century in 2015, not knowing anything about Chinese culture is testament to that. The problem itself, when translated, can be done in any language, in any location, at any time period. It's timeless for a reason!