Question

State whether the given statement is True or False :

Two numbers have $16$ as their HCF and $380$ as their LCM.

• A. True
• B. False

Answer 1

The correct option is B False

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.

i.e (HCF of the numbers must be a factor of the LCM.)

But $\frac{380}{16}=23.75$

$\text{The answer is in decimal. Thus, L.C.M. 380 is ‘not divisible’ by H.C.F. 16 of two numbers.}$$\text{The given condition is not possible.}$

$\text{hence option B is correct}$