Question

Can two numbers have 16 as HCF and 380 as LCM. Give reasons.

​

Answer 1

$\huge\red{ANSWER:-}$

Not possible to have ‘two numbers’ whose “HCF is 16 and LCM is 380”.

Solution:-

Given: 16 as their ‘HCF’ and 380 as their ‘LCM’.

We know that H.C.F. between the numbers is the ‘highest common factors’ between two numbers while L.C.M. is the ‘lowest common multiple’ of that numbers.

Two numbers with both H.C.F. as 16 and L.C.M. as 380 is not possible. 380 is the L.C.M. must be exactly divisible by 16 as their H.C.F

But 108/16=23.75

The answer is in decimal. Thus, L.C.M. 380 is ‘not divisible’ by H.C.F. 16 of two numbers.

The given condition is not possible.