Which two consecutive even numbers have an LCM of 180?

1.	Which two consecutive even numbers have an LCM of 180?
Answer» LCM of two consecutive even numbers = 180 But, HCF of two consecutive even numbers = 2 Now, product of the given number = HCF x LCM = 2 x 180 = 360 To find the two consecutive even numbers, we have to factorize 360. 360 = 2 x 2 x 2 x 3 x 3 x 5 360 = (2 x 3 x 3) x (2 x 2 x 5) = 18 x 20 ∴ The two consecutive even numbers whose LCM is 180 are 18 and 20.

Answer»

LCM of two consecutive even numbers = 180

But, HCF of two consecutive even numbers = 2

Now, product of the given number = HCF x LCM

= 2 x 180

= 360

To find the two consecutive even numbers, we have to factorize 360.

360 = 2 x 2 x 2 x 3 x 3 x 5

360 = (2 x 3 x 3) x (2 x 2 x 5)

= 18 x 20

∴ The two consecutive even numbers whose LCM is 180 are 18 and 20.

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