We consider left cancellative monoids M that are generated by their atoms S, and such that if a subset of S admits a common right multiple, then it actually admits a least

common multiple.

I could generate polyrhythmic graphs of least

common multiples or use computer models if I wanted (I didn't), but, in the end, human ears would judge the performance, so human ears should guide the learning process.

Equivalence: To develop a foundation for later algebra, students use the Snap Blocks virtual manipulative to explore equivalent expressions, common factors, and

common multiples.

Intermediate players use striped, colored cards that may be played in several locations, reinforcing

common multiples.

Students had the opportunity to take fractional amounts apart and put them back together and to develop a conceptual understanding of equivalent fractions and least

common multiples.

They will also develop a conceptual understanding of equivalent fractions and least

common multiples instead of merely memorizing rules or algorithms.

This explanation grew from his work with the drums, which clearly set the conceptual foundation for his future study of

common multiples.

For example, to find

common multiples on the graph, they notice which times tables all have points located at 12 on the y-axis.

1] Amarnth Murthy, Some notions on least

common multiples, Smarandache Notions Journal, 12(2001), 307-309.

1) n divides the least

common multiple of 1, 2, 3, .

k] denotes the least

common multiple of all positive integers from 1 to k.

t]] denote the greatest common divisor and the least

common multiple of any positive integers [x.