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.