The LCM of two numbers is 1200. Show that the HCF of these numbers cannot be 500. Why?

No, ∵ HCF should divide LCM exactly.

Using Euclid’s division lemma -

Take a = 1200 and b = 500.

a = bq + r. where q is the quotient, r is the remainder and b is the divisor.

If HCF divides LCM completely, r = 0.

Here 1200 = 500(2) + 200

r = 200

∵ r is not equal to zero.

∴ HCF does not divides LCM completely.

So this is not possible for two numbers to have HCF = 500 and LCM = 1200.