If the LCM and HCF of two numbers are equal, then the numbers must be OptionsComposite Numbers Prime NumbersEqualCo- prime Numbers

When the LCM (Least Common Multiple) and HCF (Highest Common Factor) of two numbers are equal, it indicates a special relationship between them. Here's how to analyze the options provided:

Analysis

1. LCM and HCF Definition:

   • The LCM of two numbers is the smallest number that is a multiple of both.
   • The HCF of two numbers is the largest number that divides both without leaving a remainder.

2. When LCM = HCF:

   • This situation can only occur if the two numbers are identical. In that case, both the LCM and HCF will equal the common number itself.

3. Option Analysis:

   • Composite Numbers: If both numbers are composite and equal, the LCM and HCF can equal the number, but this isn't universally true since composite numbers can be different.
   • Prime Numbers: If both numbers are the same prime number, then the LCM and HCF are equal, fulfilling the condition.
   • Co-prime Numbers: If numbers are co-prime (having no common factor other than 1), then LCM will be their product, and HCF will be 1, thus they cannot be equal.

Conclusion

From the analysis, we deduce that:

The correct answer is Prime Numbers. If the LCM and HCF of two numbers are equal, then those numbers can only be the same prime number.