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4 and 5 are co-prime so the smallest positive integer that is divisible by 4 and 5 is 4*5 = 20. Let S stand for the smallest positive integer that is divisible by 4, 5 and B.

After that the answer depends on the value of B

  • If B is co-prime with both 4 and 5 then S = 20B.
  • If B is co-prime with 4 but is a multiple of 5, then let B = 5*C. Then S = 20C.
  • If B is a multiple of 4 but is co-prime with 5, then let B = 4*D. Then S = 20D.
  • If B is a multiple of 2 but not 4, and is co-prime with 5, then let B = 2*E. Then S = 20E.
  • If B is a multiple of 2 but not 4, and is also a multiple of 5, then let B = 10*F. Then S = 20F.
  • If B is a multiple of 4 as well as of 5 then S = B.
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