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

p² + 2p, 2p⁴ + 3p³-2p², 2p³-3p²-14p

Factors of p² + 2p

=p(p + 2)

Factors of 2p⁴ + 3p³-2p²

=p²(2p² + 3p-2)

= p²(2p² + 4p-p-2)

=p²{2p(p + 2)-1(p + 2)}

=p²{(2p-1)(p + 2)}

Factors of 2p³-3p²-14p

=p(2p²-3p-14)

=p(2p²-7p + 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 p² + 2p, 2p⁴ + 3p³-2p², 2p³-3p²-14p is

p²(2p-1)(p + 2) (2p-7)