How many eggs are there in the basket?

Question

There is a basket of an eggs. The remainder is 1 When we put the eggs into the group of 2. The remainder is 2 when put the eggs in the group of 3. The remainder is 3 when we put eggs in the group of 4. The remainder is 4 and 5 respectively When we put the eggs in the group of 5 and 6. How many eggs are there in the basket?

Answer 1

Hint. If you have $n$ eggs, then $n+1$ is divisible by $2$, $3$, $4$, $5$, and $6$.