Alex will wash 18 + 12 + 17 + 13 = <<18+12+17+13=60>>60 items.
With 20 items per wash cycle, Alex will wash the clothes in 60 / 15 = 4 cycles.
With 45 minutes per cycle, the washing machine will take 45 * 4 = <<45*4=180>>180 minutes to wash the clothes.
As 1 hour has 60 minutes, the washing machine will take 180 / 60 = <<180/60=3>>3 hours to wash the clothes.
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