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Threes and Fours

Age 14 to 16 Short
Challenge Level

An integer contains only the digits $3$ and $4$, with at least one of each.
The integer is divisible by both $3$ and $4$.

What is the smallest such integer?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.