Numbers and boxes

The integers from 1 to 1000 (inclusive) are to be placed into boxes such that no box contains a number that is a multiple of another number in the same box.

What is the minimum number of boxes needed?

As an explicit example, the integers from 1 to 10 can be placed into 4 boxes while satisfying the condition:

• Box 1 - $$\{ 1 \}$$
• Box 2 - $$\{ 2, 3, 5, 7 \}$$
• Box 3 - $$\{ 4, 6, 9 , 10\}$$
• Box 4 - $$\{ 8 \}$$
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