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Common Multiples Visualization by Austen Meek

Common Multiples Visualization by Austen Meek
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2014-12-19 06:35
VectorCoordinate GeometryGeometric Construction
In collections Arithmetic: Skills & Concepts Arithmetic: Skills & Concepts Arithmetic: Skills & Concepts
This example visually demonstrates common multiples and least common multiples of numbers. It involves fundamental concepts from number theory. Using GeoGebra commands such as Textfield, Translate, and Vector, it dynamically illustrates these concepts. Suitable for students from upper elementary to middle school to learn about number theory and operations with numbers.

GeoGebra Commands & Parameters

  1. Textfield(A1) → inputBox1
  2. Textfield(A2) → inputBox2
  3. Textfield(A3) → inputBox3
  4. Translate(xAxis, u) → xAxis'
  5. Vector((C1, D1), (C1, F1)) → J1
  6. Vector((C2, D2), (C2, F2)) → J2
  7. Vector((C2, D2), (C2, F2)) → v
  8. Vector((C3, D3), (C3, F3)) → J3
  9. Vector((C4, D4), (C4, F4)) → J4
  10. Vector((C5, D5), (C5, F5)) → J5
  11. Vector((C6, D6), (C6, F6)) → J6
  12. Vector((C7, D7), (C7, F7)) → J7
  13. Vector((C8, D8), (C8, F8)) → J8
  14. Vector((C9, D9), (C9, F9)) → J9
  15. Vector((C10, D10), (C10, F10)) → J10
  16. Vector((C11, D11), (C11, F11)) → J11
  17. Vector((C12, D12), (C12, F12)) → J12
  18. Vector((C13, D13), (C13, F13)) → J13
  19. Vector((C14, D14), (C14, F14)) → J14
  20. Vector((C15, D15), (C15, F15)) → J15
  21. Vector((C16, D16), (C16, F16)) → J16
  22. Vector((C17, D17), (C17, F17)) → J17
  23. Vector((C18, D18), (C18, F18)) → J18
  24. Vector((C19, D19), (C19, F19)) → J19
  25. Vector((C20, D20), (C20, F20)) → J20
  26. Vector((C21, D21), (C21, F21)) → J21
  27. Vector((C22, D22), (C22, F22)) → J22
  28. Vector((C23, D23), (C23, F23)) → J23
  29. Vector((C24, D24), (C24, F24)) → J24
  30. Vector((C25, D25), (C25, F25)) → J25
  31. Vector((C26, D26), (C26, F26)) → J26
  32. Vector((C27, D27), (C27, F27)) → J27
  33. Vector((C28, D28), (C28, F28)) → J28
  34. Vector((C29, D29), (C29, F29)) → J29
  35. Vector((C30, D30), (C30, F30)) → J30
  36. Vector((C31, D31), (C31, F31)) → J31
  37. Vector((C32, D32), (C32, F32)) → J32
  38. Vector((C33, D33), (C33, F33)) → J33
  39. Vector((C34, D34), (C34, F34)) → J34
  40. Vector((C35, D35), (C35, F35)) → J35
  41. Vector((C36, D36), (C36, F36)) → J36
  42. Vector((C37, D37), (C37, F37)) → J37
  43. Vector((C38, D38), (C38, F38)) → J38
  44. Vector((C39, D39), (C39, F39)) → J39
  45. Vector((C40, D40), (C40, F40)) → J40
  46. Vector((C3, D3), (C3, F3)) → w
  47. Vector((C4, D4), (C4, F4)) → a
  48. Vector((C5, D5), (C5, F5)) → b
  49. Vector((G1, H1), (G1, (-0.3))) → K1
  50. Vector((G2, H2), (G2, (-0.3))) → K2
  51. Vector((G3, H3), (G3, (-0.3))) → K3
  52. Vector((G4, H4), (G4, (-0.3))) → K4
  53. Vector((G5, H5), (G5, (-0.3))) → K5
  54. Vector((G6, H6), (G6, (-0.3))) → K6
  55. Vector((G7, H7), (G7, (-0.3))) → K7
  56. Vector((G8, H8), (G8, (-0.3))) → K8
  57. Vector((G9, H9), (G9, (-0.3))) → K9
  58. Vector((G10, H10), (G10, (-0.3))) → K10
  59. Vector((G11, H11), (G11, (-0.3))) → K11
  60. Vector((G12, H12), (G12, (-0.3))) → K12
  61. Vector((G13, H13), (G13, (-0.3))) → K13
  62. Vector((G14, H14), (G14, (-0.3))) → K14
  63. Vector((G15, H15), (G15, (-0.3))) → K15
  64. Vector((G16, H16), (G16, (-0.3))) → K16
  65. Vector((G17, H17), (G17, (-0.3))) → K17
  66. Vector((G18, H18), (G18, (-0.3))) → K18
  67. Vector((G19, H19), (G19, (-0.3))) → K19
  68. Vector((G20, H20), (G20, (-0.3))) → K20
  69. Vector((G21, H21), (G21, (-0.3))) → K21
  70. Vector((G22, H22), (G22, (-0.3))) → K22
  71. Vector((G23, H23), (G23, (-0.3))) → K23
  72. Vector((G24, H24), (G24, (-0.3))) → K24
  73. Vector((G25, H25), (G25, (-0.3))) → K25
  74. Vector((G26, H26), (G26, (-0.3))) → K26
  75. Vector((G27, H27), (G27, (-0.3))) → K27
  76. Vector((G28, H28), (G28, (-0.3))) → K28
  77. Vector((G29, H29), (G29, (-0.3))) → K29
  78. Vector((G30, H30), (G30, (-0.3))) → K30
  79. Vector((G31, H31), (G31, (-0.3))) → K31
  80. Vector((G32, H32), (G32, (-0.3))) → K32
  81. Vector((G33, H33), (G33, (-0.3))) → K33
  82. Vector((G34, H34), (G34, (-0.3))) → K34
  83. Vector((G35, H35), (G35, (-0.3))) → K35
  84. Vector((G36, H36), (G36, (-0.3))) → K36
  85. Vector((G37, H37), (G37, (-0.3))) → K37
  86. Vector((G38, H38), (G38, (-0.3))) → K38
  87. Vector((G39, H39), (G39, (-0.3))) → K39
  88. Vector((G40, H40), (G40, (-0.3))) → K40
  89. Vector((C41, D41), (C41, F41)) → J41
  90. Vector((G41, H41), (G41, (-0.3))) → K41
  91. Vector((C42, D42), (C42, F42)) → J42
  92. Vector((G42, H42), (G42, (-0.3))) → K42
  93. Vector((C43, D43), (C43, F43)) → J43
  94. Vector((G43, H43), (G43, (-0.3))) → K43
  95. Vector((C44, D44), (C44, F44)) → J44
  96. Vector((G44, H44), (G44, (-0.3))) → K44
  97. Vector((C45, D45), (C45, F45)) → J45
  98. Vector((G45, H45), (G45, (-0.3))) → K45
  99. Vector((C46, D46), (C46, F46)) → J46
  100. Vector((G46, H46), (G46, (-0.3))) → K46
  101. Vector((C47, D47), (C47, F47)) → J47
  102. Vector((G47, H47), (G47, (-0.3))) → K47
  103. Vector((C48, D48), (C48, F48)) → J48
  104. Vector((G48, H48), (G48, (-0.3))) → K48
  105. Vector((C49, D49), (C49, F49)) → J49
  106. Vector((G49, H49), (G49, (-0.3))) → K49
  107. Vector((C50, D50), (C50, F50)) → J50
  108. Vector((G50, H50), (G50, (-0.3))) → K50
  109. Vector((C51, D51), (C51, F51)) → J51
  110. Vector((G51, H51), (G51, (-0.3))) → K51
  111. Vector((C52, D52), (C52, F52)) → J52
  112. Vector((G52, H52), (G52, (-0.3))) → K52
  113. Vector((C53, D53), (C53, F53)) → J53
  114. Vector((G53, H53), (G53, (-0.3))) → K53
  115. Vector((C54, D54), (C54, F54)) → J54
  116. Vector((G54, H54), (G54, (-0.3))) → K54
  117. Vector((C55, D55), (C55, F55)) → J55
  118. Vector((G55, H55), (G55, (-0.3))) → K55
  119. Vector((C56, D56), (C56, F56)) → J56
  120. Vector((G56, H56), (G56, (-0.3))) → K56
  121. Vector((C57, D57), (C57, F57)) → J57
  122. Vector((G57, H57), (G57, (-0.3))) → K57
  123. Vector((C58, D58), (C58, F58)) → J58
  124. Vector((G58, H58), (G58, (-0.3))) → K58
  125. Vector((C59, D59), (C59, F59)) → J59
  126. Vector((G59, H59), (G59, (-0.3))) → K59
  127. Vector((C60, D60), (C60, F60)) → J60
  128. Vector((G60, H60), (G60, (-0.3))) → K60
  129. Vector((C61, D61), (C61, F61)) → J61
  130. Vector((G61, H61), (G61, (-0.3))) → K61
  131. Vector((C62, D62), (C62, F62)) → J62
  132. Vector((G62, H62), (G62, (-0.3))) → K62
  133. Vector((C63, D63), (C63, F63)) → J63
  134. Vector((G63, H63), (G63, (-0.3))) → K63
  135. Vector((C64, D64), (C64, F64)) → J64
  136. Vector((G64, H64), (G64, (-0.3))) → K64
  137. Vector((C65, D65), (C65, F65)) → J65
  138. Vector((G65, H65), (G65, (-0.3))) → K65
  139. Vector((C66, D66), (C66, F66)) → J66
  140. Vector((G66, H66), (G66, (-0.3))) → K66
  141. Vector((C67, D67), (C67, F67)) → J67
  142. Vector((G67, H67), (G67, (-0.3))) → K67
  143. Vector((C68, D68), (C68, F68)) → J68
  144. Vector((G68, H68), (G68, (-0.3))) → K68
  145. Vector((C69, D69), (C69, F69)) → J69
  146. Vector((G69, H69), (G69, (-0.3))) → K69
  147. Vector((C70, D70), (C70, F70)) → J70
  148. Vector((G70, H70), (G70, (-0.3))) → K70
  149. Vector((C71, D71), (C71, F71)) → J71
  150. Vector((G71, H71), (G71, (-0.3))) → K71
  151. Vector((C72, D72), (C72, F72)) → J72
  152. Vector((G72, H72), (G72, (-0.3))) → K72
  153. Vector((C73, D73), (C73, F73)) → J73
  154. Vector((G73, H73), (G73, (-0.3))) → K73
  155. Vector((C74, D74), (C74, F74)) → J74
  156. Vector((G74, H74), (G74, (-0.3))) → K74
  157. Vector((C75, D75), (C75, F75)) → J75
  158. Vector((G75, H75), (G75, (-0.3))) → K75
  159. Vector((C76, D76), (C76, F76)) → J76
  160. Vector((G76, H76), (G76, (-0.3))) → K76
  161. Vector((C77, D77), (C77, F77)) → J77
  162. Vector((G77, H77), (G77, (-0.3))) → K77
  163. Vector((C78, D78), (C78, F78)) → J78
  164. Vector((G78, H78), (G78, (-0.3))) → K78
  165. Vector((C79, D79), (C79, F79)) → J79
  166. Vector((G79, H79), (G79, (-0.3))) → K79
  167. Vector((C80, D80), (C80, F80)) → J80
  168. Vector((G80, H80), (G80, (-0.3))) → K80
  169. Vector((C81, D81), (C81, F81)) → J81
  170. Vector((G81, H81), (G81, (-0.3))) → K81
  171. Vector((C82, D82), (C82, F82)) → J82
  172. Vector((G82, H82), (G82, (-0.3))) → K82
  173. Vector((C83, D83), (C83, F83)) → J83
  174. Vector((G83, H83), (G83, (-0.3))) → K83
  175. Vector((C84, D84), (C84, F84)) → J84
  176. Vector((G84, H84), (G84, (-0.3))) → K84
  177. Vector((C85, D85), (C85, F85)) → J85
  178. Vector((G85, H85), (G85, (-0.3))) → K85
  179. Vector((C86, D86), (C86, F86)) → J86
  180. Vector((G86, H86), (G86, (-0.3))) → K86
  181. Vector((C87, D87), (C87, F87)) → J87
  182. Vector((G87, H87), (G87, (-0.3))) → K87
  183. Vector((C88, D88), (C88, F88)) → J88
  184. Vector((G88, H88), (G88, (-0.3))) → K88
  185. Vector((C89, D89), (C89, F89)) → J89
  186. Vector((G89, H89), (G89, (-0.3))) → K89
  187. Vector((C90, D90), (C90, F90)) → J90
  188. Vector((G90, H90), (G90, (-0.3))) → K90
  189. Vector((C91, D91), (C91, F91)) → J91
  190. Vector((G91, H91), (G91, (-0.3))) → K91
  191. Vector((C92, D92), (C92, F92)) → J92
  192. Vector((G92, H92), (G92, (-0.3))) → K92
  193. Vector((C93, D93), (C93, F93)) → J93
  194. Vector((G93, H93), (G93, (-0.3))) → K93
  195. Vector((C94, D94), (C94, F94)) → J94
  196. Vector((G94, H94), (G94, (-0.3))) → K94
  197. Vector((C95, D95), (C95, F95)) → J95
  198. Vector((G95, H95), (G95, (-0.3))) → K95
  199. Vector((C96, D96), (C96, F96)) → J96
  200. Vector((G96, H96), (G96, (-0.3))) → K96
  201. Vector((C97, D97), (C97, F97)) → J97
  202. Vector((G97, H97), (G97, (-0.3))) → K97
  203. Vector((C98, D98), (C98, F98)) → J98
  204. Vector((G98, H98), (G98, (-0.3))) → K98
  205. Vector((C99, D99), (C99, F99)) → J99
  206. Vector((G99, H99), (G99, (-0.3))) → K99
  207. Vector((C100, D100), (C100, F100)) → J100
  208. Vector((G100, H100), (G100, (-0.3))) → K100

AI Drawing Prompt Reference

Create a visualization of common multiples and least common multiples for two numbers. Start by drawing the x-axis. Then, based on the input numbers, draw vertical line segments from the x-axis representing their common multiples. Next, draw a vertical line segment representing the least common multiple, also starting from the x-axis. Finally, use the translate command to move the x-axis to a new position to show the relationship between different multiples.
The prompt above was compiled from the original drawing commands and is for reference only.