The next one!

The smallest integer, $n > 1000$ , divisible by 37 is:

$n = \left \lceil \frac{1000}{37} \right \rceil \times 37 = 28 \times 37 = \boxed{1036}$

$1000 \equiv 1 \pmod{37} \\ \Rightarrow 1000+36 \equiv 1+36 \equiv 37 \equiv 0 \pmod{37} \\ \Rightarrow 1036 \equiv 0 \pmod{37}$

Hence , $1036$ is the required integer. :)

1000/37 = 27.027
37 * 0.027 = 1
1000 - 1 = 999
999/37 = 27
999 + 37 =1036
1036/37 = 28
1036 (Ans.)

3700- 37x100 1850-37x50 925-37x26 925plus37 plus 37 -999 Hence add 37 to arrive at 1036 the smallest integer above 1000

Calculator

37*30=1110 1110-74=1036

Divide 1000 by 37 .Reminder is 1.So the next Number more than 1000 divisible by 37 is 1036

37 × 3 = 111

37 × 27 = 999 < 1000

37 × 28 = 1036

or

999 + 37 = 1036

$1000=37 \times 27 + 1$

then the smallest integer $n$ divisible by $37$ is $n=37*28=1036.$