Question

Which two consecutive even numbers have an LCM of 180?

Answer 1

Two consecutive even numbers’ LCM = 180

The HCF of two consecutive even numbers, on the other hand, = 2

Now, the given number’s Product = HCF × LCM

= 2 × 180

= 360

We must factor 360 to find two consecutive even numbers.

2	360
2	180
2	90
3	45
3	15
5	5
	1

360 = (2 × 2 × 2) × (3 × 3 × 5)

= (2 × 3 × 3) × (2 × 2 × 5)

= 18 × 20

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