Shared factors

Relations are shared stepsPick two numbers. Their routes from 1 share a trunk (the gcd), then branch. Swap the branches (dashed) to complete the parallelogram and you land on the lcm. That is why a·b = gcd · lcm.
p = 2
p = 3
p = 5
p = 7
p = 11
p = 13
p ≥ 17
thick = shared trunk

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      n, spaced by log₂ n: around the hole (φ)
      depth Ω(n): through the tube (θ)

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a (2 to 64)b (2 to 64)
        
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Both routes on the torus

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