MO C–I–1 2018

An unknown number is divisible by just four numbers from the set {6, 15, 20, 21, 70}. Determine which ones.

Result

x = (Correct answer is: 6,15,21,70) Wrong answer

Solution:

6=2⋅3 15=3⋅5 20=22⋅5 21=3⋅7 70=2⋅5⋅7 LCM(6,15,20,21,70)=22⋅3⋅5⋅7=420  a=LCM(6,15,20,21,70)=420  x1=210 x2=630 x3=1050 x4=1470 x5=1890 x6=2310 x7=2730 …  d(210)=1,2,3,5,6,7,10,14,15,21,30,35,42,70,… d(630)=1,2,3,5,6,7,9,10,14,15,18,21,30,35,42,45,63,70,…  LCM(6,15,21,70)=2⋅3⋅5⋅7=210  k=LCM(6,15,21,70)=210  x=6,15,21,70

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