Can two numbers have 14 as their HCF and 204 as their LCM?

Explanation:

Definition of HCF and LCM:
HCF (Highest Common Factor) is the largest number that divides two or more numbers without leaving a remainder. LCM (Least Common Multiple) is the smallest number that is a multiple of two or more numbers.

Relationship between HCF and LCM:
For two numbers, say a and b, their product is equal to the product of their HCF and LCM. Mathematically, a * b = HCF(a, b) * LCM(a, b).

Given HCF and LCM:
In this case, the HCF is 14 and the LCM is 204. Therefore, we have 14 * x = 204, where x is the other number.

Can two numbers satisfy this condition?
To find the other number, we need to divide 204 by 14. If the result is a whole number, then we can say that two numbers can have 14 as their HCF and 204 as their LCM.

Calculation:
204 ÷ 14 = 14.57
Since the result is not a whole number, it means that two numbers cannot have 14 as their HCF and 204 as their LCM simultaneously.

Conclusion:
In this scenario, it is not possible for two numbers to have 14 as their HCF and 204 as their LCM simultaneously because the given numbers do not satisfy the relationship between HCF and LCM.