Question

Date: 18/9/page: 38 Can two numbers have 15 as thier H.C.F and 110 as their L.C.M? Give reason to justify your answer,​

Answer 1

Answer:

The HCF of two numbers is a factor of its LCM. Therefore, the LCM must be exactly divisible by the HCF of given numbers. Here, 110 (LCM) and 15 (HCF) are not exactly divisible by each other. ... No numbers can have 15 as their HCF and 110 as their LCM.

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Answer 2

Answer:

Given:-

HCF of two numbers = 15

LCM of two numbers = 110

To show:-

Can two numbers have 15 as their HCF and 110 as their LCM? Give reason to

justify your answer.

Solution:-

As We know that,

The HCF of two numbers is a factor of its LCM.

Therefore, the LCM must be exactly divisible by the HCF of given numbers.

Here, Given that:-

HCF of two numbers = 15

LCM of two numbers = 110

Here, 110 (LCM) and 15 (HCF) are not exactly divisible by each other.

Hence we can say,

No numbers can have 15 as their HCF and 110 as their LCM.

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Additional Information:-

HCF ( Highest common factor) = The largest or greatest factor common to any two or more given natural numbers is called as HCF of given numbers.

LCM ( Least common multiple ) = The smallest positive number that is a multiple of two or more numbers is called as LCM of given numbers.

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Step-by-step explanation:

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