Question

can two numbers have 12 as their HCF and 512 as their LCM? justify your answers.

Answer 1

Answer : $\bold{NO}$


Explanation -

Given :

HCF = 12

LCM = 512

let the first number = 12x

let the second number = 12y

Product of two numbers = HCF x LCM


$12x \times 12y = 12 \times 512$


$144xy = 6144$


$xy = \dfrac{6144}{144}$


$xy = 42.66$


Hence :

"xy" is not an exact value . So, two numbers cannot have 12 as their HCF and 512 as their LCM.

Answer 2

Answer:

No

Step-by-step explanation:

Given can two numbers have 12 as their HCF, and 512 as their LCM? justify your answers.

We have the property between HCF and LCM is LCM is always a multiple of HCF. HCF and LCM of two numbers should always be divisible.  

When 512 is divided by 12 we get 42 as quotient and remainder as 8. So 12 is not a factor of 512.

We can also do it as

Let two numbers be x and y

Product of two nos = lcm x hcf

 12x  x  12y = 12 x 512

   144 xy = 12 x 512

    xy = 512 x 12 / 144

     xy =   42.66