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?
Answer & explanation
Correct answer: option 1
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