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The least possible of the value of the sum of the number plus 400 would be 2.

If we let the number be 700 and we add 400 the number would be 1100. The sum being 2.

If we let the number be 601 and we add 400 the number would e 1001, the sum would also be 2.

If we try a sum of 1 (we definitely cannot have 0 as the sum of the digits),
1000 - 400 = 600 (sum of digits ≠ 7)
10,000 - 400 = 9,600 (sum of digits ≠ 7)

Therefore the smallest possible sum would be 2.