Consider three holidays whith perdiods: 6,10,15.
Obviously gcd(6,10,15)=1.
Obviously the holidays are at:
0,6,10,12,15,18,20,24,30,...and so on with cycle lcm(6,10,15)=30
Obviously there are no two holidays in distance=gcd(6,10,15)=1.
..but some people seems to think different.