Question

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

Answer 1

Given: LCM of two numbers = 1200

HCF should divide LCM exactly.

Using Euclid’s division lemma – a = bq + r. where q is the quotient, r is the remainder and b is the divisor.

Let us say, a = 1200 and b = 500.

If HCF divides LCM completely, then remainder is zero.

Here 1200 = 500(2) + 200

r = 200 ≠ 0