If M and N are two natural numbers such that (M = 51) and LCM of M and N is 255, then the HCF of M and N is:

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Detailed Solution

Concept- To solve this question, we will use the relation that “The product of two numbers will be equal to the product of their LCM and HCF” to get the value of HCF in the form of N as a variable. Then we will find the possible values of N that can give the LCM data provided in the question statement and finally, we will find the HCF in each case using the relation we obtained in the 1st step. Thus, we will obtain our desired answer.
Given, M and N are two natural numbers such that (M = 51) and LCM of M and N is 255, i.e.,

On substituting the values, we get,

We can rewrite this equation as,

Now we can find all the possible values of

.
For that we can factorise the given LCM and write it as a product of the prime factors.
On factorising, we get

On factorising 51 , we get,

So, we get

as 255 when

When

and

is given by

So, we have,

When