Problem #PRU-100606

Problems Algebra Number theory. Divisibility The greatest common divisor (GCD) and the least common multiplier (LCM). Mutually prime numbers

Problem

A valiant adventurer enters a dragon’s cave looking for the Holy Grail. She knows that Holy Grail is a chalice that is tall, made of gold, has encrusted rubies, and has an ancient inscription written on it. Upon entering, the knight discovers a long corridor of chalices, all marked with natural numbers starting from 1. He examines the first chalices and discovers, that every 10th chalice is tall, every 15th is made of gold, every 28th has encrusted rubies and every 27th has an ancient description. Assuming that is universally true for all the chalices in the cave, which chalice should the adventurer check so she doesn’t waste too much time checking all of them?