How to find the lowest common multiple of polynomials by factorization?
Let us follow the following examples to know how to find the lowest common multiple (L.C.M.) of polynomials by factorization.
Solved examples of lowest common multiple of polynomials by factorization:
1. Find out the L.C.M. of a^{2} + a and a^{3} – a by factorization.= x(x + 2), by taking common ‘x’
The common factor of the two expressions is ‘(x + 2)’.
The extra common factor in the first expression is (x - 2) and in the second expression is x.
Therefore, the required L.C.M = (x + 2) × (x - 2) × x
= x(x + 2) (x - 2)
= x[x(x + 2) + 1(x + 2)]
= x(x + 2) (x + 1)
= x × (x + 2) × (x + 1)
In both the expressions, the common factors are ‘x’ and ‘(x + 2)’; the extra common factors are ‘x’ in the first expression and ‘(x + 1)’ in the second expression.
Therefore, the required L.C.M. = x × (x + 2) × x × (x + 1)
= x^{2}(x + 1) (x + 2)8th Grade Math Practice
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