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My previous answer was wrong I overlooked one thing
Ok I did not use any formula.
The numbers have to be odd (otherwise all three will have a common factor which is 2). Now all you need is to pick 3 prime numbers lets pick 3 , 5 , 7 these are the only prime numbers less than 10 Right?
Now form three triplets
15 = 3*5
21 = 3*7
35 = 5*7
The all three taken together have no common factor