### How many eggs in the basket

A women was carrying a basket of Eggs when a passer-by bumped her and she dropped the basket and all the eggs broke, Passer-by asked her number of eggs to pay her. Women replied, I don’t remember exactly , but I do recall that whether I divided the eggs by 2,3,4,5 or 6 there was always one egg left over. When I took the eggs out in groups of seven, I emptied the basket.

Can you tell, **“How many minimum number of Eggs were there in the basket”?**

As in the previous problem we should find the least common multiple of 2,3,4,5 and 6 first, i.e. 60.

Now the the number of eggs can be 60+1, but its not completely divisible by 7.

So next possibility is 120+1, but its not completely divisible by 7 too.

So next possibility is 180+1, but its not completely divisible by 7 too.

So next possibility is 240+1, but its not completely divisible by 7 too.

So next possibility is 300+1, and its completely divisible by 7, so the minimum number of eggs in the basket should be 301.

Now the the number of eggs can be 60+1, but its not completely divisible by 7.

So next possibility is 120+1, but its not completely divisible by 7 too.

So next possibility is 180+1, but its not completely divisible by 7 too.

So next possibility is 240+1, but its not completely divisible by 7 too.

So next possibility is 300+1, and its completely divisible by 7, so the minimum number of eggs in the basket should be 301.