Question

What is the least number which when divided by $15$, $18$ and $21$ leaves remainders $2$, $5$ and $8$ respectively ?

Answer 1

The difference between the divisors and the remainders are same.
i.e., $15-2=18-5=21-8=13$
The LCM of $(15,18,21)-13=3\times 5\times 6\times 7-13$
$=630-13=617$.