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The problem can be described as LCM(LCM(LCM(1, 2), ...), 20), which finds the answer progressively. J has a primitive for computing the LCM of two numbers *. and can be inserted between each item in the range 1 to 20 using /.
*./ 1 + i.10 NB. confirm with the example 2520 *./ 1 + i.20 NB. the answer 232792560