Can two numbers have $15$ as their HCF and $175$ as their LCM? Give reasons.

Given: Two numbers.

To do: To find weather two numbers have $15$ as their HCF and $175$ as their LCM. and to explain reasons.

For 2 or more numbers, 

LCM$=$Product of highest power of each factor involved in the numbers.

HCF$=$Product of smallest power of each common factor.

We can conclude that LCM is always a multiple of HCF, i.e., 

LCM$=$ k$\times$ HCF

We are given that 

LCM $= 175$

HCF $= 15$

But in this case, LCM $\
eq k\times$ HCF.

Therefore, 2 numbers can't have LCM as $175$ and HCF as $15$.