The HCF and LCM of two numbers are 20 and 120 respectively. If one of the numbers is 50% greater than the other, then find the smaller number.

20 60 40 80

40

LCM × HCF = Product of two numbers ⇒ 20 × 120 = a × 1.5a ⇒ a2 = 20 × \(\frac{120}{1.5}\) ⇒ a2 = 1600 ∴ a = 40.