we have the numbers
2 4/7 , 2 7/15 , 2 3/11, 2 5/13, 2 2/9
convert to an improper fraction
2 4/7=2+4/7=18/7
2 7/15=2+7/15=37/15
2 3/11=25/11
2 5/13=31/13
2 2/9=20/9
Find the LCM
between 7 15 11 13 and 9
so
:LCM=7(5)(11)(13)(9)=45,045
Find out an equivalent fraction, with the same denominator
multiply 18/7 by (6,435/6,435)
(18/7)(6,435/6,435) -------> 115,830/45,045
multiply 37/15 by (3,003/3,003)
(37/15)(3,003/3,003)=111,111/45,045
multiply 25/11 by 4,095/4,095
(25/11)(4,095/4,095)=102,375/45,045
multiply 31/13 by 3,465/3,465
(31/13)(3,465/3,465)=107,415/45,045
multiply 20/9 by 5,005/5,005
(20/9)(5,005/5,005)=100,100/45,045
therefore
the greatest number is 2 4/7
(because the greatest numerator is 115,830)