使用SQL查找可从给定范围整除的最小正数

Question

例如：2520是被1到10的每个数字除以的最小正数。

请帮助我使用SQL逻辑查找1到20之间的最小正数

Answer 1

是13 693 680？http://rextester.com/APWPAS87659

假设结果是

暴力：

with
number as (
SELECT TOP (15000000) 
    CONVERT(BIGINT, ROW_NUMBER() OVER (ORDER BY s1.object_id)) as n
FROM
    sys.all_objects AS s1 
    CROSS JOIN sys.all_objects AS s2
    CROSS JOIN sys.all_objects AS s3
)
select
   min(n),
   max(n),
   min(
   case
   when n%20 + n%19 + n%18 + n%16 + n%15 + n%14 + n%13 + n%12 + n%11 + n%10 + n%9 + n%8 + n%7 + n%6 + n%5 + n%4 + n%3 + n%2 + n%1 = 0 then n
   end)
from
   number
;

==

假设解是10的倍数：

with
number as (
SELECT TOP (1500000) 
    CONVERT(BIGINT, ROW_NUMBER() OVER (ORDER BY s1.object_id)) * 10 as n
FROM
    sys.all_objects AS s1 
    CROSS JOIN sys.all_objects AS s2
    CROSS JOIN sys.all_objects AS s3
)
select
   min(n),
   max(n),
   min(
   case
   when n%20 + n%19 + n%18 + n%16 + n%15 + n%14 + n%13 + n%12 + n%11 + n%10 + n%9 + n%8 + n%7 + n%6 + n%5 + n%4 + n%3 + n%2 + n%1 = 0 then n
   end)
from
   number
;

只需快10倍。

假设结果是2520的倍数（最小的正数除以1到10的每个数字），6 000*2 520

with
number as (
SELECT TOP (6000) 
    CONVERT(BIGINT, ROW_NUMBER() OVER (ORDER BY s1.object_id)) * 2520 as n
FROM
    sys.all_objects AS s1 
    CROSS JOIN sys.all_objects AS s2
)
select
   min(n),
   max(n),
   min(
   case
   when n%20 + n%19 + n%18 + n%16 + n%15 + n%14 + n%13 + n%12 + n%11 = 0 then n
   end)
from
   number

非常快（比第一个提案快约x2520）。