If the number of ordered triplets (x,y,z) of positive integers such that L.C.M(x,y)=3375,L.C.M(y,z)=1125,L.C.M(z,x)=3375 is equal to ‘K’ then k-47 is equal to

3375=53⋅33,1125=53⋅32 Clearly, 33 is a factor of x, and 32  is factor of atleast one of y&z. This can be  done in 5 ways.    let 3a is factor of y and 3b is factor ofz then a,b=0,2or 1,2or2,2or2,0or2,1  Also,53 is a factor of atleast two of the numbers x,y,z which can be done in  3C2×4−2=10∴k=50 (  let 5a is factor of x,5b is factor of y,5c is factor of z, then possible triplets of a,b,c=0,3,3,1,3,3,2,3,3,3,3,3,3,0,33,1,33,2,33,3,03,3,13,3,2)