Question

Which two consecutive even numbers have an LCM of 180?

Answer 1

Let us suppose the two consecutive even numbers be 2x and 2x + 2.
Now, product of two numbers = HCF × LCM
⇒ (2x)(2x + 2) = 2 × 180 (HCM of two even number is 2)
⇒ (x)(2x + 2) = 180
⇒ 2x² + 2x = 180
⇒ 2x² + 2x − 180 = 0
⇒ x² + x − 90 = 0
⇒ (x − 9)(x + 10) = 0
⇒ x − 9 = 0 or x + 10 = 0
⇒ x = 9 or x = −10 (Neglecting)
Hence, the two consecutive even numbers are18 and 20.