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HCF and LCM of Three Numbers by Short Division

HCF and LCM of Three Numbers by Short Division
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2015-05-24 23:05
FunctionProbability & StatisticsGeometric Construction
In collections CBSE Class VI Maths
This example demonstrates how to find the highest common factor (HCF) and least common multiple (LCM) of three numbers using short division. Key mathematical concepts include the greatest common divisor and least common multiple in number theory. GeoGebra commands used include GCD, PrimeFactors, Append, Zip, etc. Suitable for students from upper elementary to middle school.

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

Please draw a graphic that demonstrates finding the HCF and LCM of three numbers using short division. The graphic should include three input boxes for entering three numbers. Then show the steps of short division, decomposing each number into prime factors and listing the quotients and remainders. Next, calculate the HCF and LCM results and display the final HCF and LCM values. The graphic should clearly show the calculation process and results, with the construction order being to input numbers first, then perform short division decomposition, and finally derive the HCF and LCM.
The prompt above was compiled from the original drawing commands and is for reference only.