Question : Two numbers are in the ratio 2:3 and their LCM is 180. What is the HCF of these numbers? [2 Marks] [CBSE 2023]
Doubt by Jaskirat
Solution :
Let the two numbers be 2x and 3x.
LCM = 180 (Given)
Here it should be noted that when two numbers 2x and 3x are divided then all the common factors of the two numbers are getting cancelled and we all know that these common factors are called HCF (Highest Common Factor) of the two numbers so we can say that here the HCF of two numbers 2x and 3x is x.
So, HCF = x
Now,
We know,
LCM × HCF = a×b
180×(x) = (2x)×(3x)
180×(x)=6x²
180/6=x²/x
30=x
Hence, HCF of the two numbers is 30.