Question

Find the least common multiple 36x^(2),9x^(2)-18x

Answer 1

The least common multiple of 36x^2 and 9x^2-18x is found by factoring both expressions, identifying the highest powers of common factors, and multiplying these together, resulting in LCM(36x^2, 9x^2-18x) = 36x^2(x - 2).

Step-by-step explanation:

To find the least common multiple (LCM) of the expressions 36x2 and 9x2-18x, we first factor each expression:

• 36x2 = 22 × 32 × x2
• 9x2 - 18x = 9x(x - 2) = 32 × x × (x - 2)

Next, identify the highest powers of common factors. Here, we see that:

1. 32 is a common factor and the highest power of 3 in both expressions.
2. x is a common term and the highest power of x is x2 in the first expression.

Finally, we multiply the unique factors together to find the LCM:

LCM (36x2, 9x2 - 18x) = 22 × 32 × x2 × (x - 2) = 36x2(x - 2)

This is the LCM because it includes all the factors from both expressions with the highest powers.