Find the least common multiple of (2a-1) 2, 1-4a2, and 8a3-12a2+6a-1

The LCM = - 2 (8a3 - 12a2 + 6a - 1).

Step-by-step explanation:

Least common multiple (LCM) of numbers is list the prime factors of each number, then multiply each factor by the greatest number of times it occurs in all the choosen numbers. If the same factor occurs more than once in both numbers, you multiply the factor the greatest number of times it occurs.

(2a - 1) 2:

= 2 * (2a - 1).

1 - 4a2:

Solving this quadratic equation,

-1 * (4a2 - 1) = - 1 * (a2 - 1/4).

-1 * (a - 1/2) ^2

= - 1 * (2a - 1) ^2

8a3 - 12a2 + 6a - 1:

Inputting a = 1/2,

1 - 3 + 3 - 1 = 0

So 2a - 1 is a root, dividing its root by the equation,

(2a - 1) (4a2 - 4a + 1)

Inputting 2a - 1 into 4a2 - 4a + 1,

1 - 2 + 1 = 0.

So 2a - 1 is a root, dividing its root by the equation,

(2a - 1) (2a - 1)

Therefore, 8a3 - 12a2 + 6a - 1 = (2a - 1) ^3

The LCM = - 2 (8a3 - 12a2 + 6a - 1)