Expression x2 + 6x + 9
= (x)2 + 2 × x × 3 + (3)2
x3 + 4x2 + 4x + 3 = (x + 3)(x2 + x + 1) …(iii)
common factor of eqn. (i), (ii) and (iii) = (x + 3)
Thus, required H.C.F. = (x + 3)
in eqns. (i), (ii) (iii)
= (x + 3)2 (x – 4) (x2 + x + 1)
= (x2 + 6x + 9) (x3 – x2 + x – 4x2 – 4x – 4)
Hence, required L.C.M
= (x2 + 6x + 9) (x3 – 5x2 – 3x – 4)