# [seqfan] Re: LCM of sums of digits

M. F. Hasler seqfan at hasler.fr
Fri Jun 7 18:08:37 CEST 2019

```On Thu, Jun 6, 2019 at 9:12 AM Claudio Meller wrote:

> What would happen if instead of taking only the sums of two numbers, we
> would take all the sums possible?

Foro example if the number Is 2304 we consider
> 2+3= 5   (...)

2+3+0= 5

Etc
>

Shouldn't then be the (sums of single) digits be included as well ?

El jue., 6 de jun. de 2019 01:40, Jack Brennen escribió:
>
> > There are only two solutions:  1 and 32760.
>

I agree -- considering that the LCM of an empty set is 1.

> > Verified with a Python program that tried the LCM of every set of
> > distinct positive integers <= 18.
>

FWIW, I also checked it for all the 480 divisors of LCM(2..18) as suggested
by Frank.
(Takes less than 0.01 seconds including computation of these divisors...)

It's funny that this unique* integer is so close to the frequently
encountered 2^15 = 32768*
(* at least for 10-fingered beings, which in addition chose to represent
2^3 with a symbol that's just a twist of that for 0...).
--
Maximilian

> > On 6/5/2019 11:44 PM, Frank Adams-watters via SeqFan wrote:
> > > An upper bound on such numbers is 12252240, the lcm of all numbers 2
> > through 18. In fact, any number with this property must be a divisor of
> > 12252240. There are 480 such numbers, so the problem is easily
> computable.
> > I'm feeling a bit too lazy to do it now; Harvey should be able to do
> it quickly.

> > -----Original Message-----
> > > Hello SeqFans,
> > > Jean-Marc Falcoz discovered the integer 32760 that has a  nice
> property.
> > > Make all possible sums of two digits:
> > > 3+2=5 ,  3+7=10 , (...),  6+0=6
> > > The LCM of all those sums is 32760 itself.
> > > Are there more integers like this?
> > > Best,
> > > É.
>
(reference: oeis.org/A308534)

```