1.can two numbers have 16 as their HCF and 380 as their LCM. Give reason. sir I need urgently.
Asked by Kannika Ashok | 4th Jul, 2011, 12:00: AM
There cannot be two numbers having 16 as their HCF and 380 as their LCM.
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.
Answered by | 4th Jul, 2011, 09:24: AM
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