State whether the following statement is true or false.

Two numbers can have the same HCF 18 and LCM 380.

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True

False

answer is B.

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Detailed Solution

It is given that, two numbers can have the same HCF 18 and LCM 380.
We know that the relation between HCF and LCM of any two positive integers is,
HCF

×

LCM

= a × b .

And, HCF of two numbers is always a factor of their LCM.
Here, HCF is 18 and LCM is 380.
380 is not divisible by 18.
Hence, 18 is not a factor of 380.
As a result, there are no two numbers whose HCF is 18 and their LCM is 380.
So, the given statement is false.
Hence, option (2) is correct.

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