The sum of two numbers is 392 and the sum and difference of the LCM and the HCF is equal to 1288 and 1232 respectively.  Find the difference between these two numbers?

112

     LCM + HCF = 1288 .... (i)

     LCM - HCF = 1232 .... (ii)

(i) - (ii) 2 HCF = 56

               HCF = 28

After putting value of HCF in equation (i)

LCM + 28 = 1288

LCM = 1260

HCF × Product of other factors = LCM

28 × Product of other factors = 1260

a × b = 45

↓     ↓

9     5

∴ Difference between number = (9 - 5) × 28 = 4 × 28 = 112