Grandma's Eggs

Number Theory Level 3

While I was visiting my grandma, I remembered that she had gotten a whole plantation of chickens and was now selling eggs by the crate. Out of curiosity, I asked her how many eggs she sold. She replied,

"I certainly can't count that high, but I know that if you divide the number of eggs by each integer from {2, 3, 4, ..., 10}, then you will have one egg leftover. However, if you divide the number of eggs by 11, there is no remainder!"

"Thank you, Grandma! Now, did you sell less than 30,000 eggs?"

"Why, yes, I believe I did!"

How many eggs did Grandma sell?


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