Alphametic BaseBall

Replace the letters of words with a number so that the below equation holds true

BASE +
BALL
---------
GAMES
----------




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I have thought of a number that is made up by using all the ten digits just once. Here are a few clues for you to guess my number:

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First five digits are divisible by 5.
First six digits are divisible by 6.
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Amazing Facts

Word ladder puzzle

The word ladder puzzle was invented by Lewis Carroll, author of Alice’s Adventures in Wonderland.