Question

can 2 numbers have 15 as their hcf and 175 as their lcm ?​

Answer 1

Step-by-step explanation:

Answer. NO! Two numbers cannot have HCF as 15 and LCM as 175 . Because LCM>HCF and HCF of the two numbers should divide the LCM completely.

Answer 2

Let us assume to the contrary that there exists two numbers, say ‘a’ and ‘b’ such that,

HCF(a,b) = 15 and LCM(a,b) = 175.

Note that, HCF(a,b) is a factor of both ‘a’ and ‘b’ i.e. HCF(a,b) divides both ‘a’ and ‘b’.

Also, LCM(a,b) is a multiple of both ‘a’ and ‘b’ i.e. both ‘a’ and ‘b’ divides LCM(a,b).

Therefore, HCF(a,b) divides LCM(a,b).

CONCLUSION : LCM of two (or more) numbers must be divisible by their HCF (or GCD).

But, the given values of HCF & LCM of two numbers does not satisfy this condition, since 175 is not divisible by 15.

Thus, there’s a contradiction, which means that our assumption was incorrect.

Therefore, there exist no two numbers such that their HCF & LCM are 15 & 175 respectively.