Which Value Cannot Be the HCF When the LCM Is 1200?

Video Explanation

Watch the video below for a clear explanation:

Solution

Question: The LCM of two numbers is 1200. Which of the following cannot be their HCF?

(a) 600    (b) 500    (c) 400    (d) 200

Important Property

The HCF of two numbers must always divide their LCM exactly.

Step-by-Step Checking

(a) 600

1200 ÷ 600 = 2 (integer) ✔

(b) 500

1200 ÷ 500 = 2.4 (not an integer) ✘

(c) 400

1200 ÷ 400 = 3 (integer) ✔

(d) 200

1200 ÷ 200 = 6 (integer) ✔

Final Answer

✔ Correct option: (b) 500

Conclusion

Since the HCF must divide the LCM exactly, 500 cannot be the HCF when the LCM is 1200.