Question

Can two numbers have 16 and 204 as their HCF and LCM respectively? And why?​

Answer 1

Answer:

no we can't have

Step-by-step explanation:

No. 

Let a and b be the numbers. 

Since a and b are both divisible by 16, their 

LCM must also be divisible by 16. 

But 204 = 4*51 is only divisible by 4, 

so 204 cannot be their LCM.

Alternate method :

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.

Or :

Let us see the factors of 204 = 2 x 2 x 3 x17

Factors of 14 = 2 x 7

Multiply 204 by 7 to get 1428. Its factors are 2 x 2 x 3 x7 x 17.

The two numbers are 14 and 1428. Their HCF = 14 and LCM = 1428 but not 204.

So we cannot have two numbers whose HCF = 14 and LCM = 204.

hope this helps you