Question

find the LCM and GCD for the following polynomial 21 x^y , 35 x y^​

Answer 1

ANSWER :-

Let f(x) = 21x2y and g(x) = 35xy2

f(x) = 21x2y = 3 ⋅ 7 ⋅ x2 y

g(x) = 35xy2 = 5 ⋅ 7 ⋅ x y2

L.C.M = 7 ⋅ 3 ⋅ 5 ⋅ x2 ⋅ y2

= 105 x2 y2

GCD = 7 ⋅ x ⋅ y

= 7xy

f(x) × g(x) = LCM × GCD

21x2y (35xy2) = (105 x2 y2)(7xy)

735x3y3 = 735x3y3

So, the relationship verified.