Question

If the Geometric Mean of two numbers is 16 and their HCF is 8, what is the difference between the LCM
and the HCF of the two numbers?
(1)16
(2)32
(3)8
(4)24​

Answer 1

Answer:

Difference between HCF and LCM is 24

Step-by-step explanation:

Let first number is a

second number is b

Geometric mean of a and b is $\sqrt{ab}$ = 16

so    ab = 256    ...1)

Product of HCF and LCM = product of first number and second number

  8 × LCM   = a × b

8 × LCM   = 256

so LCM = 32

then difference between HCF and LCM = 32 - 8 = 24

Answer 2

Answer and explanation:

Given : If the Geometric Mean of two numbers is 16 and their HCF is 8.

To find : What is the difference between the LCM  and the HCF of the two numbers?

Solution :

Let the numbers be a and b.

We know, Geometric Mean is 16

$G=\sqrt{ab}$

$16=\sqrt{ab}$

$ab=4$

i.e. Product of two number is 4.

HCF is 8.

We know,

Product of two number = HCF × LCM

$4=8\times LCM$

$LCM=\frac{1}{2}$

The difference between HCF and LCM is $8-\frac{1}{2}=\frac{16-1}{2}=\frac{15}{2}$