Least Common Multiple (LCM) of Polynomials

This is the continuation of the earlier topic GCD or HCF of Polynomials.

As we all know that whenever GCD is being discussed LCM also comes into picture.

LCM of two or more integers id the smallest positive integer which is exactly divisible by the given integers.

Since we have understood as to how to find the GCD of polynomials; let us also try to list the ways to find our LCM of Polynomials.


Least Common Multiple (LCM) of Polynomials: The Least Common Multiple (L.C.M) of two or more polynomials is the polynomial of the lowest degree, having smallest numerical coefficient which is exactly divisible by the given polynomial and whose coefficient of the highest degree term has the same sign as the sign of the coefficient of the highest term in their product.

Following algorithm can be used to find the LCM of two or more polynomials:-

ALGORITHM

1. Resolve each of the given polynomials into factors and express them as a product of the powers of the irreductible factors.
2. List all the irreductible factors (once only) occurring in the given polynomials. For each of these factors, find the greatest exponent in the factorised form of the given polynomials.
3. Raise each irreductible factor to the greatest exponent found in step 2 and multiply them to get the LCM