Laying Paper Strips to Find Common Multiples and LCM

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2021-10-26 15:21

① This example dynamically lays out colored paper strips to visually demonstrate the least common multiple (LCM) of two or more integers. ② Core math concepts include common multiples, least common multiple, factors and multiples, and equal spacing on a number line. ③ Construction highlights: using GeoGebra commands Polygon to draw strips, Sequence to generate consecutive strip arrangements, If to control visibility and colors, a slider m to adjust values, and multiple objects (A1, q1, a1, etc.) to build strips of different lengths for visual comparison. ④ Suitable for upper elementary to middle school students learning factors, multiples, and LCM, as well as for teacher demonstrations or student exploration to grasp the concept and computation of LCM.

GeoGebra Commands & Parameters

Polygon(A_{1}, A_{1} + (m, 0), A_{1} + (m, 1), A_{1} + (0, 1)) → q_{1}, a_{1}, f_{1}, g_{1}, h_{1}
Polygon(A_{2}, A_{2} + (m, 0), A_{2} + (m, 1), A_{2} + (0, 1)) → q_{2}, a_{2}, f_{2}, g_{2}, h_{2}
Polygon(A_{3}, A_{3} + (m, 0), A_{3} + (m, 1), A_{3} + (0, 1)) → q_{3}, a_{3}, f_{3}, g_{3}, h_{3}
Polygon(A_{4}, A_{4} + (m, 0), A_{4} + (m, 1), A_{4} + (0, 1)) → q_{4}, a_{4}, f_{4}, g_{4}, h_{4}
Polygon(A_{5}, A_{5} + (m, 0), A_{5} + (m, 1), A_{5} + (0, 1)) → q_{5}, a_{5}, f_{5}, g_{5}, h_{5}
Polygon(A_{6}, A_{6} + (m, 0), A_{6} + (m, 1), A_{6} + (0, 1)) → q_{6}, a_{6}, f_{6}, g_{6}, h_{6}
Polygon(A_{7}, A_{7} + (m, 0), A_{7} + (m, 1), A_{7} + (0, 1)) → q_{7}, a_{7}, f_{7}, g_{7}, h_{7}
Polygon(A_{8}, A_{8} + (m, 0), A_{8} + (m, 1), A_{8} + (0, 1)) → q_{8}, a_{8}, f_{8}, g_{8}, h_{8}
Polygon(A_{9}, A_{9} + (m, 0), A_{9} + (m, 1), A_{9} + (0, 1)) → q_{9}, a_{9}, f_{9}, g_{9}, h_{9}
Polygon(A_{10}, A_{10} + (m, 0), A_{10} + (m, 1), A_{10} + (0, 1)) → q_{10}, a_{10}, f_{10}, g_{10}, h_{10}
Polygon(A_{11}, A_{11} + (m, 0), A_{11} + (m, 1), A_{11} + (0, 1)) → q_{11}, a_{11}, f_{11}, g_{11}, h_{11}
Polygon(A_{12}, A_{12} + (m, 0), A_{12} + (m, 1), A_{12} + (0, 1)) → q_{12}, a_{12}, f_{12}, g_{12}, h_{12}
Polygon(A_{13}, A_{13} + (m, 0), A_{13} + (m, 1), A_{13} + (0, 1)) → q_{13}, a_{13}, f_{13}, g_{13}, h_{13}
Polygon(A_{14}, A_{14} + (m, 0), A_{14} + (m, 1), A_{14} + (0, 1)) → q_{14}, a_{14}, f_{14}, g_{14}, h_{14}
Polygon(A_{15}, A_{15} + (m, 0), A_{15} + (m, 1), A_{15} + (0, 1)) → q_{15}, a_{15}, f_{15}, g_{15}, h_{15}
Polygon(A_{16}, A_{16} + (m, 0), A_{16} + (m, 1), A_{16} + (0, 1)) → q_{16}, a_{16}, f_{16}, g_{16}, h_{16}
Polygon(A_{17}, A_{17} + (m, 0), A_{17} + (m, 1), A_{17} + (0, 1)) → q_{17}, a_{17}, f_{17}, g_{17}, h_{17}
Polygon(A_{18}, A_{18} + (m, 0), A_{18} + (m, 1), A_{18} + (0, 1)) → q_{18}, a_{18}, f_{18}, g_{18}, h_{18}
Polygon(A_{19}, A_{19} + (m, 0), A_{19} + (m, 1), A_{19} + (0, 1)) → q_{19}, a_{19}, f_{19}, g_{19}, h_{19}
Polygon(A_{20}, A_{20} + (m, 0), A_{20} + (m, 1), A_{20} + (0, 1)) → q_{20}, a_{20}, f_{20}, g_{20}, h_{20}
Polygon(B_{1}, B_{1} + (n, 0), B_{1} + (n, 1), B_{1} + (0, 1)) → r_{1}, b_{1}, k_{1}, j_{1}, i_{1}
Polygon(B_{2}, B_{2} + (n, 0), B_{2} + (n, 1), B_{2} + (0, 1)) → r_{2}, b_{2}, k_{2}, j_{2}, i_{2}
Polygon(B_{3}, B_{3} + (n, 0), B_{3} + (n, 1), B_{3} + (0, 1)) → r_{3}, b_{3}, k_{3}, j_{3}, i_{3}
Polygon(B_{4}, B_{4} + (n, 0), B_{4} + (n, 1), B_{4} + (0, 1)) → r_{4}, b_{4}, k_{4}, j_{4}, i_{4}
Polygon(B_{5}, B_{5} + (n, 0), B_{5} + (n, 1), B_{5} + (0, 1)) → r_{5}, b_{5}, k_{5}, j_{5}, i_{5}
Polygon(B_{6}, B_{6} + (n, 0), B_{6} + (n, 1), B_{6} + (0, 1)) → r_{6}, b_{6}, k_{6}, j_{6}, i_{6}
Polygon(B_{7}, B_{7} + (n, 0), B_{7} + (n, 1), B_{7} + (0, 1)) → r_{7}, b_{7}, k_{7}, j_{7}, i_{7}
Polygon(B_{8}, B_{8} + (n, 0), B_{8} + (n, 1), B_{8} + (0, 1)) → r_{8}, b_{8}, k_{8}, j_{8}, i_{8}
Polygon(B_{9}, B_{9} + (n, 0), B_{9} + (n, 1), B_{9} + (0, 1)) → r_{9}, b_{9}, k_{9}, j_{9}, i_{9}
Polygon(B_{10}, B_{10} + (n, 0), B_{10} + (n, 1), B_{10} + (0, 1)) → r_{10}, b_{10}, k_{10}, j_{10}, i_{10}
Polygon(B_{11}, B_{11} + (n, 0), B_{11} + (n, 1), B_{11} + (0, 1)) → r_{11}, b_{11}, k_{11}, j_{11}, i_{11}
Polygon(B_{12}, B_{12} + (n, 0), B_{12} + (n, 1), B_{12} + (0, 1)) → r_{12}, b_{12}, k_{12}, j_{12}, i_{12}
Polygon(B_{13}, B_{13} + (n, 0), B_{13} + (n, 1), B_{13} + (0, 1)) → r_{13}, b_{13}, k_{13}, j_{13}, i_{13}
Polygon(B_{14}, B_{14} + (n, 0), B_{14} + (n, 1), B_{14} + (0, 1)) → r_{14}, b_{14}, k_{14}, j_{14}, i_{14}
Polygon(B_{15}, B_{15} + (n, 0), B_{15} + (n, 1), B_{15} + (0, 1)) → r_{15}, b_{15}, k_{15}, j_{15}, i_{15}
Polygon(B_{16}, B_{16} + (n, 0), B_{16} + (n, 1), B_{16} + (0, 1)) → r_{16}, b_{16}, k_{16}, j_{16}, i_{16}
Polygon(B_{17}, B_{17} + (n, 0), B_{17} + (n, 1), B_{17} + (0, 1)) → r_{17}, b_{17}, k_{17}, j_{17}, i_{17}
Polygon(B_{18}, B_{18} + (n, 0), B_{18} + (n, 1), B_{18} + (0, 1)) → r_{18}, b_{18}, k_{18}, j_{18}, i_{18}
Polygon(B_{19}, B_{19} + (n, 0), B_{19} + (n, 1), B_{19} + (0, 1)) → r_{19}, b_{19}, k_{19}, j_{19}, i_{19}
Polygon(B_{20}, B_{20} + (n, 0), B_{20} + (n, 1), B_{20} + (0, 1)) → r_{20}, b_{20}, k_{20}, j_{20}, i_{20}
Sequence(Segment[((i * LCM[m, n]), 0), ((i * LCM[m, n]), 4)], i, 1, floor(Min[length1, length2] / LCM[m, n])) → l1, {}
If(B_{2} ≟ B_{1} + (n, 0), true, false) → o1
If(B_{3} ≟ B_{2}, true, false) → o2

AI Drawing Prompt Reference

Create a math teaching visualization for finding the least common multiple: show two parallel rows of colored paper strips arranged horizontally, the first row with width m (adjustable via slider) and the second row with width n, both starting aligned at 0. The strips use different colors and display common multiples along a number line above; when the two rows align at a point, that position marks the LCM of m and n, indicated by vertical line segments with LCM labels. The overall layout presents a number line structure to help students intuitively understand common multiples and least common multiple.

The prompt above was compiled from the original drawing commands and is for reference only.