Let’s find the L.

factors of ab⁴-8ab

=ab(b³-8)

=ab(b-2)(b² + 2b + 4)

Factors of a²b⁴ + 8a²b

=a²b(b³ + 8)

= a²b(b + 2)( b²-2b + 4)

Factors of ab⁴-4ab²

=ab²(b²-4)

= ab²(b + 2)(b-2)

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 ab⁴-8ab, a²b⁴ + 8a²b, ab⁴-4ab² is

a²b²(b + 2)(b-2)(b²-2b + 4)(b² + 2b + 4)

= a²b²(b³ + 8) (b³-8)