Q. 4 I3.8( 5 Votes )

# Let’s find the L.C.M. of the following algebraic expressions:

3x^{2}-15x + 18, 2x^{2} + 2x-24, 4x^{2} + 36x + 80

Answer :

factors of 3x^{2}-15x + 18

=3x^{2}-9x-6x + 18

=3x(x-3)-6(x-3)

=(3x-6) (x-3)

=3(x-2) (x-3)

Factors of 2x^{2} + 2x-24

=2(x^{2} + x-12)

=2(x^{2} + 4x-3x-12)

=2(x(x + 4)-3(x + 4))

=2(x-3) (x + 4)

Factors of 4x^{2} + 36x + 80

=4(x^{2} + 9x + 20)

=4(x^{2} + 5x + 4x + 20)

=4{x(x + 5) + 4(x + 5)}

=4(x + 5) (x + 4)

LCM is the lowest common multiple, which is the product of all the common factors taken once and the remaining factors as it is.

∴ the LCM of 3x^{2}-15x + 18, 2x^{2} + 2x-24, 4x^{2} + 36x + 80 is

12(x-2) (x-3) (x + 4) (x + 5)

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