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Can two numbers have 18 as their HCF and 380 as their LCM give reason

As we know that

HCF [a, b] × LCM [a, b] = [a × b]

18 must be factor of 380.

So, 380/18 should be a natural number.

But 380/18 is not a natural number or 380 is not divisible by 18.

So, 380 and 18 are not the LCM and HCF of any two numbers.

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Given:

HCF $= 18$

LCM $=380$

To do:

We have to check if two numbers can have 18 as their HCF and 380 as their LCM.

Solution:

HCF is the Highest common factor between two numbers and LCM is the Lowest common multiple of those numbers.

So, for a pair of numbers, LCM must be completely divisible by the HCF of those two numbers.

Therefore, if two numbers have 18 as their HCF and 380 as their LCM then, 380 must be completely divisible by 18.

Now,

$\frac{380}{18}\ =\ 21.11$

We can see that 380 is not completely divisible by 18.

So, two numbers cannot have 18 as their HCF and 380 as their LCM.

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Updated on 10-Oct-2022 13:27:08

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