Question

which two consecutive Even Numbers have an LCM of 180

Answer 1

18 and 20.
hope this will hely you for exolanation search on google it will show with explanation.

Answer 2

Answer:

18,20 are two consecutive even numbers.

Step-by-step explanation:

Given: Two consecutive even terms and LCM = 180

To find : Consecutive numbers

Let’s assume the two terms:

1st term : 2x

2nd term : 2x + 2

There is a rule which states that :

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

i.e,  $a\times b=\text{HCF} \times \text{LCM}$.......[1]

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’.

i.e, HCF= 2 ..........[2]

From [1] and [2],

$2x\times(2x+2) =\text{HCF} \times \text{LCM}$

$4x^2+4x=2 \times 180$

$x^2+x=90$

$x^2+x-90=0$

Solving the quadratic equation by middle term split we get,

$x^2+10x-9x-90=0$

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

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

x=9,−10(we discard -10 since it is negative)

Therefore, the numbers

1st term : 2x =2×9=18

2nd term : 2x + 2 =2×9+2=18+2=20

Therefore, 18,20 are two consecutive even numbers.