Prove that [ac, bc] = c[a,b]. c>0?

Question

This question is in an college number theory book.This question is located in the chapter entitled divisibilty of integars. The instructor states to use GCD (ac, bc) = c(ab) as a proving point.

Answer 1

Is [a,b]=LCM[a,b]?

If so, then:
Let (a,b)=GCD(a,b):
And observe that [m,n]=mn/(m,n).
And c>0, so c^2ab/c(a,b) is defined.

Then:

[ac,bc]=(ac)(bc)/(ac,bc) = (c^2ab)/c(a,b)= c[ab/(a,b)]=c[a,b]

Answer 2

LMNOP.