LCM of Polynomials

The Lowest Common Multiple (LCM) of two or more polynomials is the product of the polynomials of the lowest degree and the smallest numerical coefficient which are multiples of the corresponding elements of each of the given polynomials.

For example, the LCM of 4(x + 1)2 and 6(x + 1)3 is 12(x + 1)3.

The LCM of monomials is found by multiplying the LCM of numerical coefficients of each of the monomials and all variable factors with highest powers. For example, the LCM of
12x2y2z and 18x2yz is 36x2y2z since the LCM of 12 and 18 is 36 and highest powers variable factors x, y and z are x2, y2 and z respectively.

To determine the LCM of polynomials, which can be easily factorized, you express each of the polynomials as the product of factors. Then, the LCM of the given polynomials is the product of the LCM of the numerical coefficients and all other factors with their highest powers which occur in factorization of any of the polynomials.