Euclid's algorithm can be applied to real numbers, as described by Euclid in Book 10 of his "Elements". The goal of the algorithm is to identify a real number such that two given real numbers, and , are integer multiples of it: and , where and are integers. This identification is equivalent to finding an integer relation among the real numbers and ; that is, it determines integers and such that . Euclid uses this algorithm to treat the question of incommensurable lengths.