Tile factory

Extract

In The bequest of the Greeks Tobias Dantzig illustrates the Euclidean division algorithm using squares and rectangles. Although he dwells on the continued fraction expansion for a/b, where a and b are relatively prime, it is only a small step to use the Greek imagery of representing numbers by geometric figures for illustrating the algorithm in finding gcd(a,b), the greatest common divisor (or highest common factor) of two numbers a and b. Indeed, this geometric line of thinking leads to an easily programmable algorithm for directly finding lcm(a,b), the least common multiple of a and b, without first finding gcd(a,b).