Question

Least common multiple of 28(x^2+x) and 42(x^3-x)

Answer 1

The least common multiple (LCM) of 28(x^2+x) and 42(x^3-x) is 84x(x+1)(x-1).

Step-by-step explanation:

The least common multiple (LCM) of two or more numbers is the smallest number that is divisible by each of the given numbers.

To find the LCM of 28(x^2+x) and 42(x^3-x), we can first factorize each expression:

28(x^2+x) = 2^2 * 7 * x * (x+1)

42(x^3-x) = 2 * 3^1 * 7 * x * (x-1)

Next, we take the highest power of each factor that appears in either expression:

2^2 * 3^1 * 7 * x * (x+1) * (x-1)

So the LCM is 84x(x+1)(x-1).