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HCF & LCM of Two Numbers by Short Division

HCF & LCM of Two Numbers by Short Division
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2018-11-07 20:43
FunctionGeometric Construction
This example demonstrates how to calculate the Highest Common Factor (HCF) and Least Common Multiple (LCM) of two numbers using the short division method via GeoGebra. It involves core mathematical concepts like divisibility, prime factorization, the steps of short division, and the definitions of HCF and LCM. GeoGebra commands and objects used include PrimeFactors, Append, Zip, Element, Textfield, TableText, and Join. Suitable for middle school and above students to understand and master the calculation methods of HCF and LCM.

GeoGebra Commands & Parameters

  1. PrimeFactors(GCD[{a, b}]) → list1
  2. Append(1, Sequence[Product[list1, k], k, 1, Length[list1]]) → list1P
  3. Zip(a / k, k, list1P) → listA
  4. Zip(b / k, k, list1P) → listB
  5. Element(Last[listA], 1) → a'
  6. Element(Last[listB], 1) → b'
  7. Textfield(a) → inputBox1
  8. Textfield(b) → inputBox2
  9. Append(Zip[Text[p] + (UnicodeToLetter[8901]), p, Take[list1, 1, Length[list1] - 1]], Text[Element[list1, Length[list1]]]) → listTextHCF
  10. TableText({First[list1, step1], First[listA, step1 + 1], First[listB, step1 + 1]}, "|0100 vr") → text1
  11. Join({list1, Last[listA], Last[listB]}) → listLCM
  12. Append(Zip[Text[p] + (UnicodeToLetter[8901]), p, Take[listLCM, 1, Length[listLCM] - 1]], Text[Element[listLCM, Length[listLCM]]]) → listTextLCM

AI Drawing Prompt Reference

Illustrate the calculation of the Highest Common Factor (HCF) and Least Common Multiple (LCM) of two numbers using the short division method, showing the prime factorization and the product of prime factors, with corresponding quotients, to visually represent the HCF and LCM clearly labeled at each step.
The prompt above was compiled from the original drawing commands and is for reference only.