-step explanation:There is a property for HCF and LCM of two numbers, according to whichHCF × LCM = Product of the two numbers6×180 = x(x+6)1080 = x² + 6xx² + 6x - 1080 = 0This is a QUADRATIC equation, so we'll get two possible VALUES of x. We have a few methods of solving quadratic equations. I will be using the factorization method.Here, we first need to find the factors of 1080 such that their difference is 6 (since there is a negative sign before 1080; we would have found factors with a sum of 6 if there would have been a positive sign).The two factors are 30 and 36. Since the difference is +6 (middle TERM), the GREATER number must be positive and the SMALLER number, negative. Hence, we have the two numbers 36 and -30.x² + 6x - 1080 = 0x² + 36x - 30x - 1080 = 0x (x+36) -30(x+36) = 0(x+36)(x-30) = 0x + 36 = 0 or x - 30 = 0x = -36 or x = 30Since we are talking about HCF and LCM, the numbers cannot be negative. So we only have on possible option left and that is x = 30. So the numbers will be 30 and 36.