Question

Which two consecutive even numbers have an least common multiple of 180?

Answer 1

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,  .......[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],

Solving the quadratic equation by middle term split we get,

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.