Can two numbers have 18 as their HCF and 380 as their LCM give reason
As we know that Show 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. AcademicMathematicsNCERTClass 10
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More Detail 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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Can two numbers have 18 as HCF and 360 as LCM?Answer: Step-by-step explanation: HCF of two numbers is a factor of LCM of those two numbers. Here, 18 is a factor of 360 and hence it is possible that are 18 and 360 are HCF and LCM of two numbers.
Is it possible for the HCF and LCM of two numbers to be 18 and 378 respectively justify your answer?Yes. Justification: HCF of two numbers is always a factor of their LCM. But here 18 is a factor of 378. Hence Two numbers can have 18 as their HCF and 380 as their LCM.
Can two numbers have 18 as their HCF and 280 as their LCM?No, two numbers can't have 18 as their HCF and 380 as LCM because HCF of the numbers must be a factor of the LCM.
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