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