Question

Verify the following statements :
(a) If HCF of two numbers is one number itself, then their LCM is the other number.
C) The HCF of two or more numbers is a factor of their LCM.
in maths​

Answer 1

Answer:

As we know,

(i) HCF(a,b) x LCM(a,b) = a x b

If the HCF of two number say m and n, let's say is n

Then,

m x n = n x LCM(m,n)

Therefore, LCM(m,n) must have to be equal to the second number which in this condition is m

(ii) HCF(a,b) x LCM(a,b) = a x b

Further simplifying this expression,

(a x b)/HCF(a,b) = LCM=(a,b)

Therefore we can interpret this situation as

HCF(a,b) x p = LCM(a,b) (for any integer p)

Hence it is clear that HCF of two or more numbers is a factor of its LCM

I hope it's clear to you