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HCF & LCM by Short Division

HCF & LCM by Short Division
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2015-12-23 02:40
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. It involves core mathematical concepts such as divisibility, prime factorization, common multiples, and common factors. The construction utilizes GeoGebra commands and objects like PrimeFactors (prime factorization), Append (adding to a list), Zip (combining lists), Element (selecting elements), Textfield (text input), TableText (tabular display), and Join (concatenating strings). Suitable for middle school and above students to understand the calculation methods and applications of HCF and LCM, as well as prime factorization.

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

Draw the short division process for calculating the highest common factor (HCF) and least common multiple (LCM) of two numbers. Input two numbers, calculate their common factors and multiples, and display their prime factorization. Show the steps to obtain HCF and LCM from these prime factors. Display the prime factorization steps and how to calculate HCF and LCM from these steps.
The prompt above was compiled from the original drawing commands and is for reference only.