The greatest arrangement she could obtain if every flower is used is the greatest common factor of the number of roses and lilies which is 36.
Factors of :
90 : 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45 and 90.
36 : 1, 2, 3, 4, 6, 9, 12, 18, and 36
The greatest factor common to both 90 which is the number of roses and 36 which is the number of lilies is 9.
Therefore, the greatest arrangement which she Cann make using the two flowers is 9
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