19. (6 points) The teacher is preparing fruits for the party. Apples come in boxes of 20, oranges in boxes of 30, and bananas in bunches of 40. There are 50 students in the class, and each student is to receive $a$ apples, $a$ oranges, and $a$ bananas ($a$ is an integer), with no leftovers. Therefore, the teacher needs to prepare at least $\qquad$ boxes of apples, $\qquad$ boxes of oranges, and $\qquad$ bunches of bananas. (Answer in integers)
【Analysis】It is required that each student receives $a$ apples, $a$ oranges, and $a$ bananas, meaning the total number of apples, oranges, and bananas must be equal, and the total number must be a multiple of $20$, $30$, $40$, and $50$. First, find the least common multiple (LCM) of $20$, $30$, $40$, and $50$, and then, based on the number of apples, oranges, and bananas per box, the number of boxes can be determined.

【Solution】Solution: $[20,30,40,50]=600$,
Apples $600 \div 20=30$ (boxes),
Oranges $600 \div 30=20$ (boxes),
Bananas $600 \div 40=15$ (boxes).
Answer: The teacher needs to prepare at least 30 boxes of apples, 20 boxes of oranges, and 15 boxes of bananas.
Therefore, the answer is: $30,20,15$.
【Comment】The key to solving this problem is to understand that the total number of apples, oranges, and bananas must be equal, and then find the least common multiple (LCM) of $20$, $30$, $40$, and $50$ to solve the problem.