Question

can two numbers have 16 as their HCF and 204 as their LCM? reasons in support ​

Answer 1

Answer:

Answer. HCF of two numbers should be the LCM of those two numbers. So two numbers cannot have 16 as HCF and 204 as LCM.

Step-by-step explanation:

No,

Let X and Y be our two numbers,

And

X=14a

Y =14b

Where a,b are Co prime to each other

To find the LCM,

LCM = 14ab

According to question

LCM = 204

204 = 14ab

14.5714.... = ab

Because a and b are Co prime integers

a*b cannot be a fraction.

Therefore, 204 cannot be the LCM if 14 is the HCF