# Find the least integer greater than 9999 that is divisible by 3,7,13

What is the the least integer greater than 9999 that is divisible by 3,7,13 ? Any method can be used pay attention to the Euclid algorithm?

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Since you are new, I want to give some advice about the site: To get the best possible answers, you should explain what your thoughts on the problem are so far. That way, people won't tell you things you already know, and they can write answers at an appropriate level; also, people tend to be more willing to help you if you show that you've tried the problem yourself. Also, some would consider your post rude because it is a command ("Find"), not a request for help, so please consider rewriting it. – Zev Chonoles Jun 9 '13 at 18:14
A number is divisible by 3, 7 and 13 if and only if it is divisible by ... ? – anon Jun 9 '13 at 18:15
How is this related to Euclid Algorithm? – lab bhattacharjee Jun 9 '13 at 18:17
I wonder if your instructor really intended "any method" to include "ask on MSE". – Robert Israel Jun 9 '13 at 18:20
This is a question he marked extra hard and wanted us to figure out a solution by reading books or even asking people . So I am allowed to use MSE. – andrew Jun 9 '13 at 18:33

## 1 Answer

HINT: As lcm $(3,7,13)=273$ and $\frac{9999}{273}\approx 36.6$

so the answer will be $273\cdot37$

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This is so simple that it hurts...+1 – DonAntonio Jun 9 '13 at 19:45
273.37 is not an integer so its the answer correct ? – andrew Jun 10 '13 at 0:43
@andrew, $273\cdot 37$ means $273*37$ – lab bhattacharjee Jun 10 '13 at 3:33