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.