When LCM and HCF of Two Rational Numbers Are Equal

Video Explanation

Watch the video below for a clear explanation:

Solution

Question: The LCM and HCF of two rational numbers are equal. Then the numbers must be:

(a) prime    (b) co-prime    (c) composite    (d) equal

Important Property

For any two rational numbers a and b:

a × b = LCM(a, b) × HCF(a, b)

Step 1: Use the Given Condition

Given: LCM(a, b) = HCF(a, b)

Let LCM(a, b) = HCF(a, b) = k

Step 2: Apply the Formula

a × b = k × k

a × b = k²

Step 3: Draw the Conclusion

This is possible only when a = b = k.

Hence, the two rational numbers must be equal.

Final Answer

✔ The numbers must be equal.

✔ Correct option: (d) equal

Conclusion

Thus, if the LCM and HCF of two rational numbers are equal, then the two numbers themselves are equal.