**Q) **The two numbers are in the ratio of 2 : 3 and their LCM is 180. What is the HCF of the these numbers?

**Ans: **

Let us consider, the two number be 2x & 3x in the ratio of 2 : 3.

Therefore the LCM of these two numbers = 6x

Since, its given that the LCM of two numbers is 180; therefore:

6x = 180

or x = 30

Therefore, the two numbers are 60 & 90.

The HCF of 60 & 90 = 30

**Therefore, the HCF of given numbers is 30.**