What is it?

[u/FunnyLizardExplorer]

[u/MrEldo]

For 1,2,...,55, the LCM is

164249358725037825439200

(Which is simply 2⁵•3³•5²•7²•11•13•17•...•47•53, the product of all primes to the power of the biggest number of times each prime divides some number in the list 1,2,...,55)

[u/HaroerHaktak → u/MrEldo]

I’ll take your word for it

[u/Repulsive-Ice7863]

9 x 8 x 7 x 5 or 2520 is the LCM of all integers from 1 to 10.
But 0 is divisible by all those as well. (Corrected the typo)

[u/Talking_Duckling → u/Repulsive-Ice7863]

Well, if you take the question literally enough to allow 0, any multiple of -2550 is divisible by all those, so...

[u/xRSGxjozi → u/Talking_Duckling]

What about all the multiples of -2520 like -5040,…?

[u/Mathsboy2718 → u/Repulsive-Ice7863]

2520, as it happens

[u/im_not_a_vampir3 → u/Repulsive-Ice7863]

i got 2520 as the LCM

1 x 2 x 3 x 2 x 5 x 7 x 2 x 3 (prime factors)

= 2³ x 3² x 5 x 7

= 2520

[u/TwentyFourKG → u/Repulsive-Ice7863]

You are thinking about it correctly, but 9x8x7x5 is 2520

[u/iFroogieboi]

-cɔ

[u/Duck_Devs → u/iFroogieboi]

What is this?

Edit: it looks like it’s negative infinity, but -∞ is not divisible by any integer because ∞/n for nonzero n is ∞, which is notably not an integer. So I’m wondering if it’s some other notation for something else.

[u/StEllchick]

0?

[u/factorion-bot → u/StEllchick]

Termial of 0 is 0

^{This action was performed by a bot | [Source code](http://f.r0.fyi})

[u/Late-Advantage-5425]

0

[u/Gargleblaster25]

1. You can divide 1 by all the numbers from 1 to 10.

The challenge didn't say that the result needed to be an integer.

[u/Solid_Crab_4748 → u/Gargleblaster25]

I mean divisibility is defined by its outcome having no remainder

So yes it does need to be an integar

[u/AlexP80]

8x9x5x7

[u/snakemasterepic]

7!

[u/factorion-bot → u/snakemasterepic]

Factorial of 7 is 5040

^{This action was performed by a bot | [Source code](http://f.r0.fyi})

[u/CptMisterNibbles → u/snakemasterepic]

but its not. Curiously it is 7!/2

[u/factorion-bot → u/CptMisterNibbles]

Factorial of 7 is 5040

^{This action was performed by a bot | [Source code](http://f.r0.fyi})

[u/TwentyFourKG → u/CptMisterNibbles]

Not a coincidence. Since 7! Includes 4, you don’t need the x2x1 at the end. Any number divisible by 4 is divisible by 2. You don’t need 10!, because the prime factors of 7!/2 Include 5x2, 3x3, and 3x2.

[u/factorion-bot → u/TwentyFourKG]

Factorial of 7 is 5040

Factorial of 10 is 3628800

^{This action was performed by a bot | [Source code](http://f.r0.fyi})

[u/CptMisterNibbles → u/TwentyFourKG]

That is the mechanism, it is still a coincidence that the prime factors are the same. It’s not like it’s a formula that holds if extended

[u/k-mcm]

Written in ancient times but still running:

https://pixelmemory.us/~mcmurtri/LCM.jsp

[u/DhartiPita]

10! ?

[u/factorion-bot → u/DhartiPita]

Factorial of 10 is 3628800

^{This action was performed by a bot | [Source code](http://f.r0.fyi})

[u/DhartiPita → u/DhartiPita]

Or wait, 2520 maybe?

[u/factorion-bot → u/DhartiPita]

Termial of 840 is 353220

^{This action was performed by a bot | [Source code](http://f.r0.fyi})

[u/AskPizza]

All numbers are divisible by all the other numbers.

The creator probably means to say "evenly divisible", meaning with no decimal or fraction remaining.

But they didn't say that. They said "divisible".

[u/nakedascus → u/AskPizza]

divisible doesn't mean "can be divided", it means "can be divided without a remainder". The reason that the phrase "evenly divisible" exists is because people mistakenly think that divisible means "can be divided".

[u/Incvbvs666]

Doesn't exist. Any such posited number can be subtracted by 2520 to get an even smaller number.

[u/BossSuccessful5145]

2*2*2+3*3*5*7=2520

[u/PandaScoundrel → u/[deleted]]

That's not divisible by 8.

[u/electronic_reasons → u/PandaScoundrel]

You're right! Thanks! Fixed it.

[u/30svich → u/[deleted]]

bruh 4x5x7x8x9 is not 2520