Sold LLC business, when do I file taxes?

your real question seems to be "when do I need to pay in the income taxes I will owe on the income". your personal 1040 for 2024 is still due 4/15/2025

there are the safe harbor rules 

There will be no federal penalties for 2024 for not paying in enough taxes during the year if withholding
1) and timely estimated tax payments equal or exceed 90% of your 2024 tax or
2) and timely estimated tax payments equal or exceed 100% of your 2023 tax (110% if your 2023 adjusted gross income was more than $150K) or
3) the balance due after subtracting taxes withheld from 90% of your 2024 tax is less than $1,000 or
4) your total taxes are less than $1,000

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if you have a state income tax their rules usually follow the above 1 or 2 except for the %'s that must be paid in

may be different 

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using safe harbor could leave you owing a bunch come 4/15/2025. some are uncomfortable with this. any additional payment is voluntary.

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see 1040-ES worksheet (below) or use an online calculator. here is a link to one. there are others. search the web if you wish. WARNING they may not be 100% accurate since final tax laws for 2024 may not have been enacted. often with different calculators you will get different results.

https://www.aarp.org/money/taxes/1040-tax-calculator/?msockid=21e7a35e04a46bb61869b7b105606ad4 

when to pay? that depends on the period in which you earned the income

1/1-3/31/2024 was due 4/15/2024

4/1-5/31/2024 was due 6/17/2024

6/1-8/31/2024 will be due by 9/16/2024

9/1-12/31/2024 will be due by 1/15/2025

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how to pay

you can mail in form 1040-es with payment

Make your check or money order payable to “United
States Treasury.” Don’t send cash. To help process your
payment accurately, enter the amount on the right side of
the check like this: $ XXX.XX. Don’t use dashes or lines
(for example, don’t enter “$ XXX—” or “$ XXX xx/100”).
• Enter “2024 Form 1040-ES” and your SSN on your
check or money order. If you are filing a joint estimated tax
payment voucher, enter the SSN that you will show first on
your joint return.
• Enclose, but don’t staple or attach, your payment with
the estimated tax payment voucher.

also, the check/MO has your name address. note that the form itself has worksheets to calculate your 2024 tax and other ways to pay the taxes. 

https://www.irs.gov/pub/irs-pdf/f1040es.pdf 

or set up an account and pay online

https://www.irs.gov/payments 

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if you have a state income tax visit the state's website for info 

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Note that with uneven income and uneven payments it may be necessary for you to use the form 2210's Annualized Income installment worksheet to avoid penalties for 2024 if you do not meet the safe harbor rules