短除法求三数最大公约数与最小公倍数

GeoGebra 命令及参数

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