The LCM of two numbers is 28 times their HCF and the sum of their LCM and HCF is 493. The difference of the two numbers is 51. If C is the sum of the two numbers, then what is the sum of digits of C?

16

LCM =HCF ( Product of other factors)   .......(i)

LCM = HCF × 28   .....(ii)

So, Product of other factors = 28  .....(iii)

ATQ,

LCM + HCF = 493   ......(iv)

From (ii)

28HCF + HCF = 493

29 HCF = 493

HCF = 17

From (iv): LCM + 17 = 493

LCM = 476

Now,

A - B = 51                (A & B are two number)

HCF (a - b) = 51        (a & b are two other factors of A & B)

a - b = \(\frac{51}{17}\) = 3

ab = 28 (from (iii))

ab = 7× 4   (because difference of a and b is 3)

Now, HCF (a + b) = 17 (7 + 4) = 17 × 11 = 187 = 16