Question

Can two numbers have 16 as their HCF and 204 as their LCM? Give reason

Answer 1

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