Multiple choice

Find the smallest 3-digit number such that when it is divided by 8, 16, 24 and 36, it leaves a remainder of 11 in each case.

  1. 1020

  2. 1024

  3. 1030

  4. 1029

  5. 1019
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E Correct answer
Explanation

Let the smallest 3-digit number be 1000.

Now, LCM of 8, 16, 24 and 36 = 144

On dividing 1000 by 144,

Dividend = quotient x divisor + remainder

1000 = 6 x 144 + 136

So, the required number is = 1000 + (144 - 136) + 11 = 1000 + 8 + 11 = 1019.

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