The HCF and LCM of two numbers are 16 and 96 respectively and the two numbers are in ratio 2 : 3.  Find the small number?

32 36 64 16

32

LCM = HCF × (product of two other factors) Ratio of numbers is =2 : 3 (other factors) ATQ, 96 = 16 × (2R × 3R) 6 = 2R × 3R R2 = 1 ⇒ R = 1 Hence, Smallest number = 16 × 2R = 32R = 32