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:

First expression = a

= a(a + 1), by taking common ‘a’

Second expression = a

= a(a

= a(a

= a(a + 1) (a - 1), we know a

The common factors of the two expressions are ‘a’ and (a + 1); (a - 1) is the extra factor in the second expression.

Therefore, the required L.C.M. of a

First expression = x

= x

= (x + 2) (x - 2), we know a

Second expression = x

= 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)

First expression = x

= x

= x × x × (x + 2)

Second expression = x

= x(x

= x(x

= 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**8th Grade Math Practice**

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