please help me find the GCF AND LCM of a)12cd^3f^4 and 15c^3d^2f^9 b)12x^4yz^2 and 32x3y4z4 c)15p^4q^6r^4 , 20p^3q^9r^7 , and 10r^6p?

GCF is equal to the product of all prime factors in lowest order.
LCM is equal to the product of all prime factors in highest order.


(a)
12 c d^3 f^4 = 2^2 * 3 c d^3 f^4
15 c^3 d^2 f^9 = 3 * 5 c^3 d^2 f^9

GCF = 3 c d^2 f^4
LCM = 2^2 * 3 * 5 c^3 d^3 f^9 = 60 c^3 d^3 f^9


(b)
12 x^4 y z^2 = 2^2 * 3 x^4 y z^2
32 x^3 y^4 z^4 = 2^5 x^3 y^4 z^4

GCF = 2^2 x^3 y z^2 = 4 x^3 y z^2
LCM = 2^5 * 3 x^4 y^4 z^4 = 96 x^4 y^4 z^4


(c)
15 p^4 q^6 r^4 = 3 * 5 p^4 q^6 r^4
20 p^3 q^9 r^7 = 2^2 * 5 p^3 q^9 r^7
10 r^6 p = 2 * 5 p r^6

GCF = 5 p r^4
LCM = 2^2 * 3 * 5 p^4 q^9 r^7 = 60 p^4 q^9 r^7

a)12cd^3f^4 and 15c^3d^2f^9

12cd^3f^4 = 2^2 x 3 x c x d^3 x f^4

15c^3d^2f^9 = 3 x 5 x c^3 x d^2 x f^9

GCF = 3 x c x d^2 x f^4

= 3cd^2f^4

LCM = 2^2 x 3 x 5 x c^3 x d^3 x f^9

= 60c^3d^3f^9


b)12x^4yz^2 and 32x3y4z4

12x^4yz^2 = 2^2 x 3 x x^4 x y x z^2

32x3y4z4 = 2^5 x x^3 x y^4 x z^4

GCF = 2^2 x x^3 x y x z^2

= 4x^3yz^2

LCM = 32x^4y^4z^4



c)15p^4q^6r^4 , 20p^3q^9r^7 , and 10r^6p

15p^4q^6r^4 = 3 x 5 x p^4 x q^6 x r^4

20p^3q^9r^7 = 2^2 x 5 x p^3 x q^6 x r^4

10r^6p = 2 x 5 x r^6 x p

GCF = 5 x p x r^4

= 5pr^4

LCM = 2^2 x 3 x 5 x p^4 x q^6 x r^6

= 60p^4q^6r^6