9514 1404 393
Answer:
1. (rose bunches, lily bunches) ∈ {(2, 3), (4, 6), (6, 9), (8, 12)}. The least is (2, 3).
2. 6(2+3); 14(3+1); 9(4+3)
Explanation:
I like Euclid's algorithm for finding the greatest common factor (GCF): divide the larger number by the smaller, and note the remainder. If the remainder is zero, the smaller is the GCF; if not, use the remainder in place of the larger number and repeat.
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1. The GCF of 8 and 12 is 4, so the least common multiple is ...
LCM(a, b) = ab/GCF(a, b)
LCM(8, 12) = 8·12/4 = 24
24 roses is 2 bunches; 24 lilies is 3 bunches. Up to 8 bunches of roses can be ordered to keep the number less than 100.
The florist could have ordered these numbers of bunches (roses, lilies):
(2, 3), (4, 6), (6, 9), (8, 12)
The least order is 2 bunches of roses and 3 bunches of lilies.
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2.
A. GCF = 6, so the factored form is 6(2+3)
B. GCF = 14, so the factored form is 14(3+1)
C. GCF = 9, so the factored form is 9(4+3)