Question

what is the least common multiple of x, x-1, and x-2? i think that its x(x-1)(x-2) but i dont knowww

Answer 1

yes, yes it is x*(x-1)*(x-2)

Answer 2

It's not x(x-1)(x-2) for all x, since LCM(4,4-1,4-2)=LCM(4,3,2)=12≠4*3*2=24. But you have the right idea. The thing is that if x is even, x-2 must be even and so they share the factor 2, this means that the LCM is x(x-1)(x-2)/2 when x is even. Your formula is correct when x is odd, since only x-1 is even and they can't share any other factors (since the spacing between them is too small to account for any other common factor than 2).

Answer 3

@dape ...? given that we dont know if x is even or odd or a variable, the point stands that LCM = x*(x-1)*(x-2)