Question

What is the greatest $3-$digit number, which is exactly divisible by $3,5,6$ and$7$?

Answer 1

The least number which is exactly divisible by $3,5,6$ and$7$ is LCM$(3,5,6,7)=210$.

So, all the multiples of $210$ will be exactly divisible by $3,5,6$ and$7$.

Thus, such greatest $3-$digit number is $210\times 4=840$.