Consecutive difficulty

Algebra Level 3

The number 15 can be written as 7 + 8 or 4 + 5 + 6 or 1 + 2 + 3 + 4 + 5 (the sum of 2 consecutive integers, 3 consecutive integers and 5 consecutive integers).

Find the smallest positive integer that can be expressed as the sum of 3 consecutive integers, 5 consecutive integers and 7 consecutive integers.

Taken from 3rd round of the 2013 South African Junior Maths Olympiad

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