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Geometric Interpretation of LCM and GCD

Geometric Interpretation of LCM and GCD
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2017-11-20 00:49
VectorCoordinate GeometryOptimizationGeometric Construction
This example demonstrates how to geometrically interpret the concepts of the Greatest Common Divisor (GCD) and the Least Common Multiple (LCM). It involves core mathematical concepts such as GCD, LCM, vectors, coordinate geometry, and geometric construction. The construction uses GeoGebra commands like Intersect, CurveCartesian, GCD, Point, Sequence, Polygon, and PointIn. It is suitable for high school and university-level mathematics courses to visualize and understand number theory concepts.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. CurveCartesian((a * t), (b * t), t, 0, 1) → c
  3. GCD(a, b) → d
  4. Point(L_3) → F
  5. Point(L_2) → G
  6. Point(L_3) → H
  7. Point(L_2) → I
  8. Point(L_3) → J
  9. Point(L_2) → E
  10. Point(L_2) → K
  11. Point(L_3) → L
  12. Point(L_3) → N
  13. Sequence((b / d * n), n, 1, d, 1) → L_1
  14. Polygon(K, N, B, A) → q1, k, n, b_1, a_1
  15. Polygon(D, C, B, A) → q2, d_1, c_1, b_2, a_2
  16. Intersect(c_1, k) → M
  17. PointIn(q1) → Pontoq1
  18. Sequence(n / d, n, 1, d - 1, 1) → L_4