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.

Correct answer:

x = 6,15,21,70

Step-by-step explanation:

6=23 15=35 20=225 21=37 70=257 LCM(6,15,20,21,70)=22357=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)=2357=210  k=LCM(6,15,21,70)=210  x=6,15,21,70



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