Question

the lcm of two consecutive even number is 180. find the number ​

Answer 1

Answer:

Let the number be 2x and 2x+2

A/q,

2x(x+1) = 180

x²+x-90 = 0

x²+10x-9x-90 = 0

x(x+10)-9(x+10) = 0

(x+10)(x-9) = 0

x = 9

Numbers are = 18 & 20 . (Ans)

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Answer 2

Answer:

★First number = 18 and Second Number = 20 ★

Step-by-step explanation:

Given:

• LCM of consecutive even numbers is 180

To Find: Find the two consecutive even numbers

Solution: Let the 1st consecutive even number is 2x and 2nd consecutive even number is 2x + 2

→ If ‘a’ and ‘b’ are two numbers, then their product is equal to the product of their LCM and HCF

→We can logically say that the HCF of any two consecutive even numbers is always equal to ‘2’ provided that the smallest no. is at least ‘2’.

According to the question

$\small\implies{\sf }$ 2x (2x + 2 ) = HCF x LCM

$\small\implies{\sf }$ 4x² + 4x = 2 x 180

$\small\implies{\sf }$ x² + x = 90

$\small\implies{\sf }$ x² + x – 90 = 0

★By middle term Splitting★

$\small\implies{\sf }$ x² + 10x – 9x – 90 = 0

$\small\implies{\sf }$ x(x + 10) – 9(x+10) = 0

$\small\implies{\sf }$ (x+10)(x–9)

So, x = 9 and –10( Discard –10 because it is negative)

∴ Numbers = 2x = 2 x 9 = 18

and 2x + 2 = 2 x 9 + 2 = 10+2 = 20