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Threes, Fives and Sevens

Math brain teasers require computations to solve.


Puzzle ID:#28578
Fun:*** (2.19)
Difficulty:*** (2.96)
Submitted By:shenqiangAcn****!!
Corrected By:kiss




Which is the smallest natural number that satisfies the following conditions:

(1) Its digits consist only of, and only of 3's, 5's and 7's.
(2) Its digital sum is divisible by 3, 5 and 7.
(3) The number itself is divisible by 3, 5 and 7.

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