GCF and LCM: word problems

Read each problem and solve:

Carol is making flower arrangements. He has 15 roses and 30 daisies. If Carol wants to make all the arrangements identical and have no flowers left over, what is the greatest number of flower arrangements that she can make?

*1. Determine the prime factorization of each number:*

*15=3·5*

90=2·3^{2}·5

*2. Take the prime numbers that appears in all the factorizations. (Remember taking the lowest number of times they appear)*

Prime numbers selected: 3 and 5

3. GCF(15,90)=3·5
*The greatest number of flower arrangements that she can make is 15.*

Peter sells cards in packs of 12 and envelopes in packs of 27. If Martha wants the same number of each, what is the minimum number of cards that she will have to buy?

1. Determine the prime factorization of each number:

*2. Take the prime numbers that appears in all the factorizations. (Remember taking the highest number of times they appear). Prime numbers selected: 2 and 3*

*3. LCM(12,27) = 2*^{2}·3^{3} = 108
*The minimum number of cards that she will have to buy is 108.*

Robert walks his dog every two days. He gives his dog a bath once a week. Today, Robert walked his dog and then gave her a bath. How many days will pass before he does both shores on the same day?

1. Determine the prime factorization of each number:

*2. Take the prime numbers that appears in all the factorizations. (Remember taking the highest number of times they appear). Prime numbers selected: 2 and 7*

*3. LCM(2,7) = 2·7 = 14*
*There will pass 14 days befores he does both shores on the same day.*