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Can two numbers have 16 as their HCF and 380 as their LCM? Give reason.
By BYJU'S Exam Prep
Updated on: September 25th, 2023
No, two numbers cannot have 16 as their HCF and 380 as their LCM. The HCF and LCM of two numbers should be perfectly divisible which means they leave no remainder except zero. This is because HCF divides the two numbers whereas LCM is always divisible by the two numbers as it is their multiple.
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Difference Between HCF and LCM
HCF means the Highest Common Factor. HCF is the largest number that divides two or more numbers perfectly. On the other hand, LCM is the Least Common Multiple. It is the smallest number which can be a multiple of two or more numbers.
HCF divides two or more numbers whereas in the case of LCM, it is the numbers that have to perfectly divide the LCM. In order for two numbers have 16 as their HCF and 380 as their LCM, it is important that HCF divides LCM perfectly leaving zero as a remainder.
Two Numbers with 16 as HCF and 380 as LCM
The two numbers that have 16 as HCF and 380 as LCM should be perfectly divisible. To check whether this is the case or not, let us divide the two and check what is the reminder.
LCM = 380
HCF = 16
HCF/LCM = 380/16
= 23.75
The remainder is not zero when HCF is divided with LCM.
Hence, two numbers will not have 16 as their HCF and 380 as their LCM as they are not completely divisible.
Summary:
Can two numbers have 16 as their HCF and 380 as their LCM? Give reason.
No, it is not possible for two numbers to have 166 as HCF and 380 as LCM. This is because upon dividing HCF with LCM the remainder derived is not zero. As HCF is known to divide two or more numbers whereas LCM is divisible by two or more numbers. They both should be perfectly divisible which in this case is not true.
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