Question
Mon July 04, 2011 By: Kannika Ashok

1.can two numbers have 16 as their HCF and 380 as their LCM. Give reason. sir I need urgently.

Expert Reply
Mon July 04, 2011
There cannot be two numbers having 16 as their HCF and 380 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 = 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 arive at a contradiction.
 
Thus, there cannot exist two natural numbers having 16 as their HCF and 380 as their LCM.
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