How many eggs did the old lady have?

Once upon a time, and old lady went to sell her vast quantity of eggs at the local market.

When asked how many she had, she replied:

Son, I can't count past 100 but I know that.

If you divide the number of eggs by 2 there will be one egg left.
If you divide the number of eggs by 3 there will be one egg left.
If you divide the number of eggs by 4 there will be one egg left.
If you divide the number of eggs by 5 there will be one egg left.
If you divide the number of eggs by 6 there will be one egg left.
If you divide the number of eggs by 7 there will be one egg left.
If you divide the number of eggs by 8 there will be one egg left.
If you divide the number of eggs by 9 there will be one egg left.
If you divide the number of eggs by 10 there will be one egg left.

Finally. If you divide the Number of eggs by 11 there will be NO EGGS left!

How many eggs did the old lady have?

Answer is 27720.

lcm of 2,3...10 is 2520

2520 +1 = 2521 gives 1 as remainder if you divide any of number between 2 and 10. But 2521 is not divisible by 11. so 2521 is not the right answer.
2520 x 2 +1 = 5041 this is also not divisible by 11
...
2520 x 11 +1 = 27,721 is divisible by 11.

[COLOR="Blue"]James,

i like your way of approach....

your anwer is correct...But no need to multiply the 2520 by11....

2520 x 10 + 1 = 25201.

This is also the correct answer.

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suresh[/COLOR]

Suresh,
Actually my answer is wrong. 2520 x 11 +1 will give 1 as remainder when we divide this by 11. :(

I got the same number too..Agrre with you James..

I would say 10 ! +1 = 3628801 would also be correct