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Well, darling, the number you're looking for is 23. When you divide 23 by 5, you get a remainder of 3, and when you divide it by 3, you get a remainder of 2. So, there you have it, 23 is the sassy little number you're after.
3 divided by 2 has a remainder of 1. Which is 1 less than 2.
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24 is answer.
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The largest possible number for a remainder is 1 less than the number of the divisor, so it is 5.