Join the Joint

Can you solve the below algebraic mathematical equation?

(J+O+I+N+T)3 = JOINT




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When I divide it by 6, the remainder is 5.
When I divide it by 7, the remainder is 6.
When I divide it by 8, the remainder is 7.
When I divide it by 9, the remainder is 8.
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When I looked for a smaller number with this property I couldn't find one.

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Jigsaw puzzles

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