Find the smallest 8-digit number which gives 15 as a remainder when divided by…

Let us first find out the LCM of 38,22 and 16.

⇒ LCM(22,38,16)

⇒ 2 × 11 × 19 × 8 = 3344

Hence, every number which is divisible by 3344 is automatically divisible by 38, 22 and 16.

Now we divide 10000000 which is the least number of 8 digits to find out if it is divisible by 3344

We need 10001904 to make is completely divisible by 3344.

Hence, since 15 is the remainder which is left in every case, hence, we can say that 10001904 + 15

I.e. 10001919 is the least number which when divided by 38, 22 and 16 leaves a remainder of 15 in every case.