# [seqfan] Re: LCM of sums of digits

Jack Brennen jfb at brennen.net
Thu Jun 6 06:23:52 CEST 2019

```There are only two solutions:  1 and 32760.

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

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-----
> From: Harvey P. Dale <hpd at hpdale.org>
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Sent: Wed, Jun 5, 2019 9:43 pm
> Subject: [seqfan] Re: LCM of sums of digits
>
>      No additional terms up to 10^7.
>      Best,
>      Harvey
>
>
> -----Original Message-----
> From: SeqFan <seqfan-bounces at list.seqfan.eu> On Behalf Of Éric Angelini
> Sent: Wednesday, June 5, 2019 6:05 PM
> To: Sequence Discussion list <seqfan at list.seqfan.eu>
> Subject: [seqfan] LCM of sums of digits
>
> 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
> 3+6=9
> 3+0=3
> 2+7=9
> 2+6=8
> 2+0=2
> 7+6=13
> 7+0=7
> 6+0=6
> The LCM of all those sums is 32760 itself.
> Are there more integers like this?
> Best,
> É.
>
>
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```