Question

lesson 1.6p ~ common factors and multiples
name____ period__ date____
find the greatest common factor of each set of numbers.

1. 3,9
2. 12,16
3. 15,25
4. 14,35
5. 18,54
6. 10,75

find the least common multiple (lcm) of each pair of numbers.

1. 3 and 5
2. 6 and 8
3. 3 and 4
4. 8 and 10
5. 12 and 16
6. 10 and 12
7. karen washes light clothes every five days. she washes dark clothes every six days. if she washed both light and dark clothes today, how many days until she once again washes both light and dark clothes on the same day?
8. courtney has 27 chocolate chip cookies and 36 oatmeal raisin cookies. she needs to arrange them on trays. she doesnt want to combine either type of cookies and she wants the same number on each tray. what is the largest number of cookies she can have on each tray?
9. andrew has 48 country cds and 72 rock cds. he wants to arrange them on shelves so that the two types of cds are separate, but he wants the largest number of cds on a shelf as possible. how many cds should he put on each shelf?
10. josh visits his parents every eight days. he visits his brother every twelve days. if he visited his parents and his brother today, how many days until josh visits both his parents and his brother again on the same day?

Explanation:

Step1: Find GCF of 3, 9

List factors: Factors of 3 are 1, 3. Factors of 9 are 1, 3, 9. GCF is 3.

Step2: Find GCF of 12, 16

Prime - factorize: $12 = 2\times2\times3$, $16=2\times2\times2\times2$. Common factors are $2\times2 = 4$.

Step3: Find GCF of 15, 25

Prime - factorize: $15 = 3\times5$, $25 = 5\times5$. GCF is 5.

Step4: Find GCF of 14, 35

Prime - factorize: $14 = 2\times7$, $35 = 5\times7$. GCF is 7.

Step5: Find GCF of 18, 54

Since $54\div18 = 3$, GCF is 18.

Step6: Find GCF of 10, 75

Prime - factorize: $10 = 2\times5$, $75 = 3\times5\times5$. GCF is 5.

Step7: Find LCM of 3 and 5

Since 3 and 5 are prime to each other, $LCM(3,5)=3\times5 = 15$.

Step8: Find LCM of 6 and 8

Prime - factorize: $6 = 2\times3$, $8 = 2\times2\times2$. $LCM(6,8)=2\times2\times2\times3=24$.

Step9: Find LCM of 3 and 4

Since 3 and 4 are prime to each other, $LCM(3,4)=3\times4 = 12$.

Step10: Find LCM of 8 and 10

Prime - factorize: $8 = 2\times2\times2$, $10 = 2\times5$. $LCM(8,10)=2\times2\times2\times5 = 40$.

Step11: Find LCM of 12 and 16

Prime - factorize: $12 = 2\times2\times3$, $16 = 2\times2\times2\times2$. $LCM(12,16)=2\times2\times2\times2\times3 = 48$.

Step12: Find LCM of 10 and 12

Prime - factorize: $10 = 2\times5$, $12 = 2\times2\times3$. $LCM(10,12)=2\times2\times3\times5 = 60$.

Step13: LCM of 5 and 6

Since 5 and 6 are prime to each other, $LCM(5,6)=5\times6 = 30$ days.

Step14: GCF of 27 and 36

Prime - factorize: $27 = 3\times3\times3$, $36 = 2\times2\times3\times3$. GCF is $3\times3 = 9$ cookies per tray.

Step15: GCF of 48 and 72

Prime - factorize: $48 = 2\times2\times2\times2\times3$, $72 = 2\times2\times2\times3\times3$. GCF is $2\times2\times2\times3 = 24$ CDs per shelf.

Step16: LCM of 8 and 12

Prime - factorize: $8 = 2\times2\times2$, $12 = 2\times2\times3$. $LCM(8,12)=2\times2\times2\times3 = 24$ days.

Answer:

1. 3
2. 4
3. 5
4. 7
5. 18
6. 5
7. 15
8. 24
9. 12
10. 40
11. 48
12. 60
13. 30 days
14. 9 cookies
15. 24 CDs
16. 24 days