Is it possible to have two numbers whose HCF is 18 and LCM is 760? Give reason.

No, ∵ HCF does not divided LCM exactly

Using Euclid’s division lemma -

Take a = 760 and b = 18.

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

If HCF divides LCM completely, r = 0.

Putting the values -

Here 760 = 18(42) + 4

⇒ r = 4

∵ r is not equal to zero

∴ HCF does not divides LCM completely.

So this is not possible for two numbers to have HCF = 18 and LCM = 760.