Question

Can two number have 12 as their HCF and 512 as their LCM? justify your answer

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

can two numbers have 12 as thier HCF and 512 as their LCM justify your answer