Is it possible that H.C.F. and L.C.M. of two numbers are 18 and 380respectively?Justify

We know that LCM is the least common multiple and HCF is the highest common factor of the given numbers.

Therefore, LCM is a multiple and the HCF is a factor of the given numbers.

This means HCF must be a factor of the LCM

In the given case, if 18 is the HCF and 380 is the LCM of two numbers then 18 must be a factor of 380.

18 must divide 380

But, 18 is not a factor of 380

So it’s not possible to have two numbers whose HCF is 18 and LCM is 380.