Math Help (2 questions)?

Question

Find the LCM of this pair of monomials: 6m^2, 22mn (the ^2 means squared)

Suppose y varies directly with x. Write an equation relating x and y: y= -150 when x= 25

Answer 1

The prime factors of 6 are 3 * 2, and of 22 are 2 * 11.

The LCM of the numbers is therefore 3 * 2 * 11 = 66.

m^2 and mn have LCM m^2 n.

The LCM of 6m^2 and 22mn is therefore 66m^2 n.

As y varies directly with x, y = kx ...(1)

where k is constant.

Putting x = 25 and y = - 150:

- 150 = 25k

k = - 6.

Substituting this value in (1):

y = - 6x.