Question

can two numbers have 16 as their H.C.F and 380as their L.CM give reason.
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Answer 1

Answer:

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 = 16 x 380

Now, for 16 to be the HCF of a and b, both a and b must be the multiple of 16.

So, let a be the smallest multiple of 16, that is 16 itself.

So, 16 x b = 16 x 380

This gives b = 380

 

So, a = 16 and b = 380

But, the HCF of these two numbers is 4 and not 16.

Thus, a cannot be equal to 16. 

Also, if we take any bigger multiple of 16, then also we will arrive at a contradiction.

 

Thus, there cannot exist two natural numbers having 16 as their HCF and 380 as their LCM.