Question

The hcf of two number is 4 and their LCM is 36,if one number is 12 find the other number?

Answer 1

Heya user,

Let the no.s be a & b;

Then, HCF [ a, b ] = 4
=> a = 4m and b = 4n; such that m does not divide n

Now, LCM [ a,b ] = 36;
==> 4m | 36 & 4n | 36
==> m | 9 & n | 9;

So, possible values satisfying above criteria are m = 1,n = 9;
but then, neither of 4m or 4n is equal to 12

Soo, their exists no such pair ( a, b ) such that the above criteria is followed.

Answer 2

I know ,
a concept that ,
if two numbers a and b are given then ,
LCM{a, b} × HCF{a, b } = a × b

but if we apply it here,
We get
Both numbers are equal e.g 12 .
Means LCM = 12 , and HCF = 12

Now, Let's try this by using basic theory,
Let other number is P .
If HCF of P and 12 is 4
It mean P must be multiple of 4
so, we can write P = 4n where, n is prime number.

Now, other number is 4n
LCM of 4n and 12 = 36 .
this is possible when n = 9/2, 9 etc
But if we take n = 9 then HCF = 4 is invalid .
and if we take 9/2 then also HCF = 4 is invalid .

So, we only say that
Other number can't be possible for the condition .