Why Do We Use lP+mQ+nR=0 in the Solution of dx/P=dy/Q=dz/R?

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Dx/P = dy/Q = dz/R why we take lP+mQ+nR=0 and then solve?

why we take lP+mQ+nR = 0 in solution of dx/P=dy/Q=dz/R i-e ldx+mdy+ndz/(lP+mQ+nR) .. when lP+mQ+nR = 0 the expression goes to infinity .. how then we take integral of ldx+mdy+ndz as lx+my+nz= C. kindly clear
 
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Let the constant function be dk=dx/P = dy/Q = dz/R. Then we have
ldx+mdy+ndz= (lP+mQ+nR)dk = 0. Hence the solution.
 

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