Can two number have 16 as their HCF and 380 as their LCM ? Give reason
Answers
Answered by
101
HCF - Highest Common Factor
For two numbers, their HCF is the largest number which divides both.
LCM - Least Common Multiple
For two numbers, their LCM is the smallest number which is a multiple of both.
Now, HCF divides both numbers. And both numbers perfectly divide LCM.
So, HCF must perfectly divide LCM.
In other words, for LCM÷HCF, remainder must be zero.
Here, LCM = 380
And, HCF = 16
Clearly, 380/16 = 23.75 (remainder not zero)
Thus, there do not exist two numbers whose HCF is 16 and LCM is 380
For two numbers, their HCF is the largest number which divides both.
LCM - Least Common Multiple
For two numbers, their LCM is the smallest number which is a multiple of both.
Now, HCF divides both numbers. And both numbers perfectly divide LCM.
So, HCF must perfectly divide LCM.
In other words, for LCM÷HCF, remainder must be zero.
Here, LCM = 380
And, HCF = 16
Clearly, 380/16 = 23.75 (remainder not zero)
Thus, there do not exist two numbers whose HCF is 16 and LCM is 380
Answered by
43
We are given that LCM=16 & HCF=380
Since the LCM of two numbers is a factor of their HCF.....
Therefore here 380 must be a factor of 16....
380/16 gives 23 as quotient nd 12 as remainder,
i.e. it is not the factor of 16...
No two numbers cannot have 16 as LCM and 380 as HCF...
Hope it helps u...!!!!....
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