One night the king couldn’t sleep, so he went down into the royal kitchen, where he found a bowl full of mangoes. Being hungry, he took 1/6 of the mangoes. Later that same night, the queen was hungry and couldn’t sleep. She, too, found the mangoes and took 1/5 of what the king had left. Still later, the first prince awoke, went to the kitchen, and ate 1/4 of the remaining mangoes. Even later, his brother, the second prince, ate 1/3 of what was then left. Finally, the third prince ate 1/2 of what was left, leaving only five mangoes for the servants. How many mangoes were originally in the bowl?.