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HCF & LCM of Three Numbers by Prime Factorization

HCF & LCM of Three Numbers by Prime Factorization
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2018-05-27 21:55
Geometric Construction
This example demonstrates how to calculate the Highest Common Factor (HCF) and Least Common Multiple (LCM) of three numbers using prime factorization. It involves core mathematical concepts like prime factorization, HCF, and LCM. The construction utilizes GeoGebra commands and objects such as Factors, Unique, Sort, Zip, KeepIf, Product, If, Textfield, and LaTeX to visualize prime factors, compute HCF and LCM, and display results. Suitable for middle school and above students to understand and master the calculation methods of HCF and LCM.

GeoGebra Commands & Parameters

  1. Factors(b) → M2
  2. Unique(PrimeFactors[b]) → listB
  3. Factors(a) → M1
  4. Unique(PrimeFactors[a]) → listA
  5. Factors(c) → M3
  6. Unique(PrimeFactors[c]) → listC
  7. Sort(Union[Union[listA, listB], listC]) → listPrime
  8. Zip(If[Defined[IndexOf[k, listB]], Element[M2, IndexOf[k, listB], 2], 0], k, listPrime) → listB2
  9. Zip(If[Defined[IndexOf[k, listC]], Element[M3, IndexOf[k, listC], 2], 0], k, listPrime) → listC2
  10. Zip(If[Defined[IndexOf[k, listA]], Element[M1, IndexOf[k, listA], 2], 0], k, listPrime) → listA2
  11. Zip({k, Min[{m, n, p}]}, k, listPrime, m, listA2, n, listB2, p, listC2) → listHCF
  12. KeepIf(Element[k, 2] ≠ 0, k, listHCF) → listHCF'
  13. Product(Zip[Element[k, 1]^(Element[k, 2]), k, listHCF']) → resultHCF
  14. If(listHCF' ≟ {}, 1, resultHCF) → resultHCF'
  15. Zip(((Element[p, 1] * If[Element[p, 2] ≠ 1, (("^{" * Element[p, 2]) * "}")]) * If[{p} ≠ Last[M1], UnicodeToLetter[8901], ""]), p, M1) → listTextA
  16. Textfield(a) → inputBox1
  17. Zip(((Element[p, 1] * If[Element[p, 2] ≠ 1, (("^{" * Element[p, 2]) * "}")]) * If[{p} ≠ Last[M2], UnicodeToLetter[8901], ""]), p, M2) → listTextB
  18. Textfield(b) → inputBox2
  19. Zip(((Element[p, 1] * If[Element[p, 2] ≠ 1, (("^{" * Element[p, 2]) * "}")]) * If[{p} ≠ Last[listHCF'], UnicodeToLetter[8901], ""]), p, listHCF') → listTextHCF
  20. Zip({k, Max[{m, n, p}]}, k, listPrime, m, listA2, n, listB2, p, listC2) → listLCM
  21. Zip(((Element[p, 1] * If[Element[p, 2] ≠ 1, (("^{" * Element[p, 2]) * "}")]) * If[{p} ≠ Last[listLCM], UnicodeToLetter[8901], ""]), p, listLCM) → listTextLCM
  22. LaTeX("\text{LCM= }" + (Sum[listTextLCM])) → textLCM
  23. Textfield(c) → inputBox3
  24. Zip(((Element[p, 1] * If[Element[p, 2] ≠ 1, (("^{" * Element[p, 2]) * "}")]) * If[{p} ≠ Last[M3], UnicodeToLetter[8901], ""]), p, M3) → listTextC
  25. Product(Zip[Element[k, 1]^(Element[k, 2]), k, listLCM]) → resultLCM

AI Drawing Prompt Reference

Illustrate the prime factorization of three numbers and calculate their highest common factor (HCF) and least common multiple (LCM). First, factorize each number into prime factors and identify all unique prime factors. Then, calculate the HCF by taking the minimum power of common prime factors across all numbers, and the LCM by taking the maximum power of all prime factors. Finally, display the prime factorization of each number, the HCF, and the LCM using text.
The prompt above was compiled from the original drawing commands and is for reference only.