find the lcm of
x^2-2x-3     ,    x^2-5x+6
can anyone answer this fast please

Dear Student,

Let P(x) = x²-2x-3 and G(x) = x²-5x+6
Now, P(x) = x²-2x-3 = x²-3x+x-3 = x(x-3)+1(x-3) = (x-3)(x+1)
and G(x) = x²-5x+6 = x²-3x-2x+6 = x(x-3)-2(x-3) = (x-3)(x-2)

Thus, the L.C.M of P(x) and G(x) i.e. the L.C.M of (x-3)(x+1) and  (x-3)(x-2) is (x-3)(x-2)(x+1)

Hence, the required L.C.M of P(x) and G(x) is (x-3)(x-2)(x+1)

Regards