Question

Can two numbers have 25 and 7 as their lcm and hcf? give reason​

Answer 1

Answer:

175

Step-by-step explanation:

lcm of 7,25 is 7*25/1

lcm of 7,25 is 175/1

175

Answer 2

Answer:

There cannot be two numbers having 7 as their HCF and 25 as their LCM.

Reason:

We know that the product of two numbers is equal to the product of their LCM and HCF.

Let the two numbers be a and b.

Then, a x b = HCF x LCM

a x b = 7×25

Now, for 7 to be the HCF of a and b, both a and b must be the multiple of 25

So, let a be the smallest multiple of 7, that is 7 itself.

So, 7 x b = 7×175

This gives b = 175

So, a = 7 and b = 175

But, the HCF of these two numbers is 1 and not 7

Thus, a cannot be equal to 7

Also, if we take any bigger multiple of 7, then also we will arrive at a contradiction.

Thus, there cannot exist two natural numbers having 7 as their HCF and 25 as their LCM.

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