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HCF & LCM of Three Numbers by Short Division by Ronan Downes

HCF & LCM of Three Numbers by Short Division by Ronan Downes
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2020-07-25 10:19
InequalityGeometric Construction
This example demonstrates how to calculate the Highest Common Factor (HCF) and Least Common Multiple (LCM) of three numbers using the short division method. Key math concepts involved include GCD, LCM, and the short division process. GeoGebra commands and objects used in the construction are GCD, PrimeFactors, Append, Zip, Element, Join, Textfield, and TableText. Suitable for middle school and above, this resource helps students understand and apply the methods for calculating HCF and LCM.

GeoGebra Commands & Parameters

  1. GCD({a, b, c}) → hcf
  2. PrimeFactors(GCD[{a, b, c}]) → list1
  3. Append(1, Sequence[Product[list1, k], k, 1, Length[list1]]) → list1P
  4. Zip(a / k, k, list1P) → listA
  5. Zip(b / k, k, list1P) → listB
  6. Zip(c / k, k, list1P) → listC
  7. Element(Last[listA], 1) → a'
  8. Element(Last[listB], 1) → b'
  9. Element(Last[listC], 1) → c'
  10. Join({PrimeFactors[GCD[a', b']], PrimeFactors[GCD[b', c']], PrimeFactors[GCD[c', a']]}) → list3
  11. Zip(If[Mod[a', k] ≟ 0, k, 1], k, list3) → list3a
  12. Textfield(a) → inputBox1
  13. Textfield(b) → inputBox2
  14. Textfield(c) → inputBox3
  15. Zip(If[Mod[b', k] ≟ 0, k, 1], k, list3) → list3b
  16. Zip(If[Mod[c', k] ≟ 0, k, 1], k, list3) → list3c
  17. Append(1, Sequence[Product[list3a, k], k, 1, Length[list3a]]) → list3aP
  18. Append(1, Sequence[Product[list3b, k], k, 1, Length[list3b]]) → list3bP
  19. Append(1, Sequence[Product[list3c, k], k, 1, Length[list3c]]) → list3cP
  20. Zip(a' / k, k, list3aP) → listA'
  21. Zip(b' / k, k, list3bP) → listB'
  22. Zip(c' / k, k, list3cP) → listC'
  23. Join({list1, list3, Last[listA'], Last[listB'], Last[listC']}) → listLCM
  24. Append(Zip[Text[p] + (UnicodeToLetter[8901]), p, Take[list1, 1, Length[list1] - 1]], Text[Element[list1, Length[list1]]]) → listTextHCF
  25. Append(Zip[Text[p] + (UnicodeToLetter[8901]), p, Take[listLCM, 1, Length[listLCM] - 1]], Text[Element[listLCM, Length[listLCM]]]) → listTextLCM
  26. TableText({First[listA, step1 + 1], First[listB, step1 + 1], First[listC, step1 + 1]}, "|10000 _01 vr") → text1
  27. TableText({First[listA', step2 + 1], First[listB', step2 + 1], First[listC', step2 + 1]}, "|10000 _01 vr") → text2
  28. TableText({First[list1, step1]}, "vr") → text1a
  29. TableText({First[list3, step2]}, "vr") → text2a

AI Drawing Prompt Reference

Draw the highest common factor (HCF) and least common multiple (LCM) of three numbers a, b, and c. First, input the three numbers a, b, and c. Then, calculate their highest common factor and decompose it into prime factors. Next, compute the quotients of each number divided by the highest common factor and further process these quotients to obtain the final HCF and LCM. Finally, display all prime factors and the HCF and LCM results as text.
The prompt above was compiled from the original drawing commands and is for reference only.