One of the most important and conceptual question from real numbers chapter in which we have given that the LCM of two numbers is 1200 and we have to show that the HCF of these numbers cannot be 500 and we have to give the explanation of this.

Kindly give me a detailed solution of this question

RS Aggarwal, Class 10, chapter 1E, question no 17

## Given : LCM of two numbers =1200

HCF should decide 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 The HCF divides LCM completely , then remainder is zero.

here 1200=500(2)+200

r=200≠0

So,HCF of these numbers can not be 500