find LCM if product of 2 no. is 180 and HCF is 6
Answers
Step-by-step explanation:
There is a property for HCF and LCM of two numbers, according to which
HCF × LCM = Product of the two numbers
6×180 = x(x+6)
1080 = x² + 6x
x² + 6x - 1080 = 0
This 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 = 0
x² + 36x - 30x - 1080 = 0
x (x+36) -30(x+36) = 0
(x+36)(x-30) = 0
x + 36 = 0 or x - 30 = 0
x = -36 or x = 30
Since 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.
Step-by-step explanation:
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