Question

can two numbers have 16 as their HCF and 204 as their LCM

Answer 1

No. 
Let a and b be the numbers. 
Since a and b are both divisible by 16, their 
LCM must also be divisible by 16. 
But 204 = 4*51 is only divisible by 4, 
so 204 cannot be their LCM.