Q. 5 B4.2( 5 Votes )

# Let’s find the G.C.D and L.C.M. of the following expressions:

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

Answer :

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

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

=3y(y-3)-6(y-3)

=(3y-6) (y-3)

=3(y-2) (y-3)

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

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

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

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

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

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

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

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

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

=4(y + 5)(y + 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 3y^{2}-15y + 18, 2y^{2} + 2y-24, 4y^{2} + 36y + 80 is 12(y-2)(y + 5)(y + 4)(y-3)

GCD is the greatest common divisor, which is equal to the product of all the common divisors.

∴ the GCD is 1 as no other factor is common.

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