From the data $x=6k_{1}and x=8k_{2}$ So let x=24a similarly, y=30b z=40c given $\boxed{x<y<z}$ 24a<30b<40c 12a<15b<20c LCM(24a,30b,40c)=2400 LCM(12a,15b,40c)=1200 Let c=30 so LCM(12a,15b)=1200 LCM(4a,5b)=400 Let b=80 So, possible values of a=1,2,4,5,10,20,50,100 so here are 8 triplets. Putting different values of c and b we can get all the triplets satisfying the condition. Hope I'm not wrong