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Can two numbers have 18 as their HCF and 380 as their LCM?
By BYJU'S Exam Prep
Updated on: September 25th, 2023
No, the two numbers cannot have 18 as their HCF and 380 as their LCM. No, the LCM must be a factor of the HCF of two numbers. Therefore, only if 18 is a factor of 380 is the condition described above viable. However, we can see that it is not 380. Therefore, it is impossible to have two numbers with the same HCF (18) and LCM (380).
Table of content
Properties of LCM and HCF
Property 1:
Any two provided natural numbers’ LCM and HCF products are equal to the sum of the numbers given.
HCF x LCM = Product of the Numbers
Let’s say A and B are two different numbers.
HCF (A & B) × LCM (A & B) = A × B
Property 2:
Co-prime numbers have an HCF of 1. The product of the supplied co-prime numbers is therefore the LCM of those numbers.
LCM of Co-prime Numbers = Product Of The Numbers
Property 3:
LCM and HCF of Fractions:
HCF of fractions = HCF of Numerators / LCM of Denominators
LCM of fractions = LCM of Numerators / HCF of Denominators
Property 4:
A number’s HCF cannot ever be bigger than one of the given figures.
Property 5:
The LCM of any pair of numbers or more will never be less than one of the specified numbers.
Summary:
Can two numbers have 18 as their HCF and 380 as their LCM?
The two numbers cannot have an HCF of 18 and an LCM of 380. It is because the LCM of two numbers has to be a factor of the HCF of two numbers. So only if the value 18 is a factor of 380, the given sentence will be true.
