Q. 4 F4.4( 7 Votes )

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

p^{2} + 2p, 2p^{4} + 3p^{3}-2p^{2}, 2p^{3}-3p^{2}-14p

Answer :

Factors of p^{2} + 2p

=p(p + 2)

Factors of 2p^{4} + 3p^{3}-2p^{2}

=p^{2}(2p^{2} + 3p-2)

= p^{2}(2p^{2} + 4p-p-2)

=p^{2}{2p(p + 2)-1(p + 2)}

=p^{2}{(2p-1)(p + 2)}

Factors of 2p^{3}-3p^{2}-14p

=p(2p^{2}-3p-14)

=p(2p^{2}-7p + 4p-14)

=p{p(2p-7) + 2(2p-7)}

=p(p + 2)(2p-7)

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 p^{2} + 2p, 2p^{4} + 3p^{3}-2p^{2}, 2p^{3}-3p^{2}-14p is

p^{2}(2p-1)(p + 2) (2p-7)

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