The LCM of two consecutive even numbers is 544.find the two numbers
Answers
Answer:
Step-by-step explanation:
Let the two consecutive even numbers be
A = 2x and
B = (2x + 2)
Now The rule states that product of 2 numbers is always equal to the HCF and LCM of those 2 numbers
HCF of 2x and 2x + 2 = 2, coz at the very least those two even numbers will have their HCF as 2.
So, A x B = LCM x HCF
2x * (2x + 2) = 2 * 544
2x^2 + 4x = 2 * 544
The two numbers are (32,34) or (-34,-32).
Given:
The LCM of two consecutive even numbers is 544.
To Find:
The two numbers.
Solution:
Let the consecutive even numbers be 2a and 2a+2.
⇒x = 2a
⇒y = 2a+2
The Highest Common Factor of two or more numbers is the highest number among all the common factors of these numbers.
HCF of x and y will be 2 because HCF for any two consecutive even numbers is always 2.
As we know, the product of the LCM and HCF of two numbers is equal to the product of the two numbers.
Therefore,
⇒LCM x HCF = 2a(2a+2)
⇒544 x 2 = 2a(2a+2)
⇒544 =2a*2a + 2a*2
⇒1088 = 4a² + 4a
⇒4a² + 4a - 1088 = 0
⇒a² + a - 272 = 0
⇒ a = 16 or -17
Therefore, numbers are (32,34) or (-34,-32).
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