Can you help me find LCM? Please!!! Due tomorrow?

Question

A. LCM of u^2-81 and u^2+12u+27

B. z^3+10z^2+25z and z^2-10z

C. 35x^2+175x and 7x^2+63x+140

Thank u vey much for helping.

Answer 1

A.) u^2-81 = (u-9)(u+9) and u^2+12u+27=(u+9)(u+3), so LCM=(u+9)

B.) z(z+5)^2 and z(z-10), so LCM=z

C.) 35x(x+5) and 7(x+5)(x+4), so LCM=(x+5)

Answer 2

A. LCM of u^2-81 and u^2+12u+27

Step1: Factor both u^2-81 and u^2+12u+27

u^2-81 = (u + 9)(u - 9)

u^2+12u+27 = (u + 9)(u + 3)

Step2: Analyze the factors. Notice that there's the factor (u + 9) in both set of factors; that is (u + 9) is common to both set.

Step3: The LCM is the multiple of factors where common factors appear only once; Thus the factors of the LCM would be:

(u + 9)(u - 9)(u + 3) Answer

The LCM is usually more useful in its factored form, so you don't have to expand it by distribution anymore.

B. z^3+10z^2+25z and z^2-10z

z^3+10z^2+25z = z(z^2 + 10z + 25) = z(z + 5)(z + 5)

z^2-10z = z(z - 10)

LCM: z(z + 5)(z + 5)(z - 10) Answer

C. 35x^2+175x and 7x^2+63x+140

35x^2+175x = 5(7)(x)(x + 5)

7x^2+63x+140 = 7(x^2 + 9x + 20) = 7(x + 5)(x + 4)

LCM: 7(x + 5)(5x)(x + 4) = 35x(x + 5)(x + 4) Answer

Note: The answers given by the two answerers above are NOT the LCM, but the common factor. Trust me.

To illustrate with numbers:

What's the least common multiple (LCM) of 8 and 12?

8 = 2 * 2 * 2

12 = 2 * 2 * 3

Therefore, the LCM would be: 2 * 2 * 2 * 3 = 24

although the greatest common factor (GCF) is: 2 * 2 = 4

Answer 3

factor first

A. (u+9)(u-9)  and (u+9)(u+3)

gives u the common factor of (u+9)

B.  z(z+5)(z+5)  and z(z-10)

gives u the common factor of z

C.  35x(x+5)  and 7(x+5)(x+4)

gives u the common factor of 7(x+5)