Question

for each question, write out enough multiples of each number to find the least common multiple. circle it.

1. 5:

6:

1. 3:

24:

1. 14:

4:
derek shopping for hot dogs and buns. he is surprised to find that the hot dogs come in packs of 8, while the buns come in packs of 12. how many hot dogs and buns will derek have to buy if he wants to have the same number of each?

Explanation:

Step1: List multiples of 5

$5, 10, 15, 20, 25, 30, 35,...$

Step2: List multiples of 6

$6, 12, 18, 24, 30, 36,...$

Step3: Identify shared smallest multiple

LCM(5,6) = 30
---

Step4: List multiples of 3

$3, 6, 9, 12, 15, 18, 21, 24,...$

Step5: List multiples of 24

$24, 48, 72,...$

Step6: Identify shared smallest multiple

LCM(3,24) = 24
---

Step7: List multiples of 14

$14, 28, 42, 56, 70, 84,...$

Step8: List multiples of 4

$4, 8, 12, 16, 20, 24, 28, 32,...$

Step9: Identify shared smallest multiple

LCM(14,4) = 28
---

Step10: List multiples of 8

$8, 16, 24, 32,...$

Step11: List multiples of 12

$12, 24, 36,...$

Step12: Identify shared smallest multiple

LCM(8,12) = 24

Answer:

1. 5: $5, 10, 15, 20, 25, 30$; 6: $6, 12, 18, 24, 30$; LCM = $\boldsymbol{30}$
2. 3: $3, 6, 9, 12, 15, 18, 21, 24$; 24: $24$; LCM = $\boldsymbol{24}$
3. 14: $14, 28$; 4: $4, 8, 12, 16, 20, 24, 28$; LCM = $\boldsymbol{28}$

Derek needs to buy $\boldsymbol{24}$ hot dogs and $\boldsymbol{24}$ buns (3 packs of hot dogs, 2 packs of buns)