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On the number line above, the segment from 0 to 1 has been divided into fifths, as indicated by the large tick marks, and also into sevenths, as indicated by the small tick marks. What is the LEAST possible distance Z between any two of the tick marks?  Select.
A) 1/70 B) 1/35 C) 2/35 D) 1/12 E) 1/7
divisions are 0 1/7 2/7 3/7 4/7 5/7 6/7 1   1/5 2/5 3/5 4/5 5/5   expressing the same in terms of the lcm of 5,7 ,i.e 35   0 7/35 14/35 21/35 28/35 35/35   5/35 10/35 15/35 20/35 25/35 30/35   by comparing the divisions with each other we can see 1/35 is the shortest possible distance between any two selected divisions.   Z=1/35   Answer is 1/35.
<result>B</result>
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On the number line above, the segment from 0 to 1 has been divided into fifths, as indicated by the large tick marks, and also into sevenths, as indicated by the small tick marks. What is the LEAST possible distance Z between any two of the tick marks?