Question

can two numbers have 10 as their HCF and 300 as their LCM? Give reason​

Answer 1

Yes, we can have 10 as HCF and 300 as LCM of any two natural numbers.

This is explained as follow :-

In mathematics, there is a rule that thej HCF of any two number must be a factor of LCM or LCM must be a multiple of HCF.

i.e. LCM ÷ HCF gives remainder zero

If this is not satisfied then the given condition is wrong.

e.g.

Two numbers can have 12 as LCM and 4 as HCF because 12 is divisible by 4 while two numbers cannot have 16 as LCM and 3 as HCF because 3 is not factor of 16.

Now in the question

HCF is a factor of LCM i.e. 10 is a factor of 300

Hence two numbers can be exist i.e. real number because it satisfy the condition.