Can two numbers have 18 as their HCF and 380 as their LCM?

By Ritesh|Updated : November 5th, 2022

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).

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.

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