What will be the sum of digit of smallest number of four digit which when divided by 16, 19 and 38 leaves the remainder 6 in each case?

Given:

The smallest 4 digit number divided by 16, 19 and 38

and remainder is 6 in each case.

Calculation:

LCM of 16, 19 and 38,

⇒ 16 = 2 x 2 x 2 x 2

⇒ 19 = 19 x 1

⇒ 38 = 2 x 19 x 1

⇒ LCM = 2 x 2 x 2 x 2 x 19 = 304

We know that the smallest number of four digit = 1,000 

When 1,000 divided by 304 then remainder is 88.

So, smallest four digit number which is divided by 304 = 1000 + (304 - 88)

⇒ 1216

Now required number is leaves remainder 6,

so required number = 1216 + 6

⇒ 1222

Sum of digit of 1222 = 1 + 2 + 2 + 2

⇒ 7

∴ Required sum is 7.