Math, asked by avika52, 1 year ago


30. Can two numbers have 16 and 204 as their H.C.F. and L.C.M. respectively? And why?​

Answers

Answered by saurav2015das
2

 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.


saurav2015das: Please mark it as brainliest
Answered by srk33
3

No, two no. have 16 and 204 as their not h.c.f & l.c.m respectively...

Bcz. 16 is not a factor of 204...

...hope you get ur ans..


avika52: thanks
srk33: Wlcm bro
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