Find two consecutive even numbers whose lcm is 312
Answers
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 * 312
x ∗ (2x + 2) = 312
2x² + 2x - 312 = 0
x² + x - 156 = 0
x² + 13x - 12x - 156 = 0
x (x+13) - 12 (x+13) = 0
(x-12) (x+13) = 0
x = 12 , -13
ignoring negative value.
Our 1 st number is 2x = 2 x 12 = 24
2nd is 2x + 2 = 24 + 2 = 26
Answer:
Step-by-step explanation:
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Secondary School Math 15+8 pts
Find two consecutive even numbers whose lcm is 312
Report by Kumarsanket5903 13.08.2018
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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 * 312
x ∗ (2x + 2) = 312
2x² + 2x - 312 = 0
x² + x - 156 = 0
x² + 13x - 12x - 156 = 0
x (x+13) - 12 (x+13) = 0
(x-12) (x+13) = 0
x = 12 , -13
ignoring negative value.
Our 1 st number is 2x = 2 x 12 = 24
2nd is 2x + 2 = 24 + 2 = 26