Answer:
(x-4)(x-6)(x+3) or in more compressed form x³-7x²-6x+72
Explanation:
To find the L.C.M, w first factorize each of the expressions.
x²-10x+24
Two numbers that when added give -10 but when multiplied give 24
will be, -4 and -6
Thus the expression becomes:
x²-4x-6x+24
x(x-4)-6(x-4)
=(x-4)(x-6)
Let us factorize the second expression.
x²-x-12
Two numbers when added give -1 and when multiplied give -12
are 3 and -4
Thus the expression becomes: x²-4x+3x-12
x(x-4)+3(x-4)
(x-4)(x+3)
Therefore the LCM between (x-4)(x-6) and (x-4)(x+3)
will be
(x-4)(x-6)(x+3)
We can multiply the expression as follows.
(x-4)(x-6)
x²-6x-4x+24 = x²-10x+24
(x+3)(x²-10x+24)
=x³-10x²+24x+3x²-30x+72
=x³-7x²+-6x+72