We de ne a class of Lyndon words, called Christo el-Lyndon words. We show that they are in bijection with n-tuples of relatively prime natural numbers. We give a geometrical interpretation of these words. They are linked to an algorithm of Euclidean type, admitting an extension to n-tuples of real numbers; we show that if the algorithm is periodic, then these real numbers are algebraic of degree at most n and that the associated multidimensional continued fraction converges to these numbers.