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Can two numbers have 16 as their HCF and 380 as their LCM? Give reason.
Given:
HCF $=$ 16
LCM $=$ 380
To do: Here we have to check if two numbers can have 16 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 16 as their HCF and 380 as their LCM then, 380 must be completely divisible by 16.
Now,
$\frac{380}{16}\ =\ 23.75$
We can see that 380 is not completely divisible by 16.
So, two numbers can't have 16 as their HCF and 380 as their LCM.
Updated on: 10-Oct-2022
2K+ Views
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