Find the lowest common multiple (LCM) of the following expressions:

1. [tex] (x-4)(x+4) [/tex] and [tex] x^2-y^2 [/tex]

2. [tex] (x-2)^2 [/tex] and [tex] x^3-8 [/tex]

3. [tex] 3ab(a-b)^2 [/tex] and [tex] 2a^2b(a-b) [/tex]

4. [tex] x^3-54x^2+36x-8 [/tex] and [tex] 9x^2+9x-10 [/tex]

5. [tex] x^4-4 [/tex] and [tex] 2x^3-4x^2+4x [/tex]

6. [tex] a^2-a-2 [/tex] and [tex] a^x+a [/tex]

7. [tex] y^3-x^3 [/tex], [tex] 32x^2(y^2-x^2) [/tex], and [tex] 48(xy^4-x^3y^2) [/tex]

8. [tex] x^4+2px^3+p^2x^2 [/tex] and [tex] x^4+p^3x [/tex]

9. [tex] 3x^3+81 [/tex], [tex] x^2+2x-3 [/tex], and [tex] 3x^3-27x [/tex]

10. [tex] x^3-b^3a^2-b^2 [/tex] and [tex] a^6-b^6 [/tex]

11. [tex] x^2-x-1 [/tex], [tex] x^6-1 [/tex], and [tex] x^3-1 [/tex]

Additionally, find the LCM of the expressions [tex] a^2-12a+35 [/tex] and [tex] a^2-8a+7 [/tex].

Find another expression similar to [tex] 1^2-5m-14 [/tex] such that the LCM with [tex] (-7) [/tex] is [tex] m^3-10m^2+11m+70 [/tex].

Lastly, find the highest common factor (HCF) and LCM of:

- [tex] 4a^2-4 [/tex], [tex] 6(a^2-a-2) [/tex], and [tex] 12(a^2+3a-10) [/tex]

- [tex] 3x^2-3xy-2y^2 [/tex], [tex] 6x^2+xy-y^2 [/tex], and [tex] 3x^2-7xy+2y^2 [/tex]

- [tex] (c+a)-b(b+c) [/tex], [tex] b(a+b)-c(c+a) [/tex], and [tex] c(b-c)-a(a-b) [/tex]

- [tex] -q^2+2pq-1 [/tex], [tex] q^2-p^2+2q+1 [/tex], and [tex] p^2-q^2+2p-1 [/tex]

- [tex] -5x-4 [/tex], [tex] 8x^2-2x-15 [/tex], and [tex] 12x^2-43x+35 [/tex]