好望角234 2022-9-24 16:56
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top11 2022-9-25 17:18
[quote]原帖由 [i]好望角234[/i] 於 2022-9-24 16:56 發表 [url=https://www.discuss.com.hk/redirect.php?goto=findpost&pid=552340892&ptid=30782264][img]https://www.discuss.com.hk/images/common/back.gif[/img][/url]
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Let the number be N.
Then N = 14a + 3 = 20b + 3 = 35c + 3 where a, b, c are integers.
That means, N - 3 = 14a = 20b = 35c.
Because N - 3 is a common multiple of 14, 20, 35, we consider the L.C.M. of 14, 20, 35:
５｜１４，２０，３５
[color=#ffffff].....[/color]└————————
７｜１４， ４， ７
[color=#ffffff].....[/color]└————————
２｜ ２， ４， １
[color=#ffffff].....[/color]└————————
１， ２， １
L.C.M. = 5 × 7 × 2 × 1 × 2 × 1 = 140
The least possible value of N - 3 = 140.
The least possible value of N = 143.