IKMC 2027 - Grades 5-6 - Self-study SET 2 - Thematic Batch 3 Question 27

How many ordered tuples (a,b,c,d,e) satisfy all these conditions? a is 2 or 1/2; b is 3 or 1/3; c is 4 or 1/4; d is 5 or 1/5; e is 6 or 1/6; and a×b×c×d×e is an integer.