Divisible By 2,3,4,7

Question

What is the least positive number that is divisible by 2 if after added 2, divisible by 3 after added 3, divisible by 4 after added 4 and divisible by 7 after added 7.

Answer 1

See that the smaller number that is divisible by 2, 3, 4 and 7 is: 2^2•3•7 Then, all of these numbers can be writed like you want to add, for example: 2^2•3•7 = 7•k Then 7•k+7 = 7(k+1) and it's divisible by 7.

Answer 2

$N1=84$

$N1+2=86$ is divisible by 2

$N1+3=87$ is divisible by 3

$N1+4=88$ is divisible by 4

$N1+7=91$ is divisible by 7

$N2=168$

$N2+2=170$ is divisible by 2

$N2+3=171$ is divisible by 3

$N2+4=172$ is divisible by 4

$N2+7=175$ is divisible by 7