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

Asked by Rajarshi Basu | 23rd May, 2012, 08:01: PM

Expert Answer:

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.

Answered by  | 23rd May, 2012, 10:57: PM

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