Q. 173.6( 9 Votes )

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

Answer :

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.


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