最小公倍数

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Arjay is planning a barbecue. He is at the store to buy hot dogs and hot dog buns. The hot dogs come in packs of 8 while the buns come in packs of 6. At least how many packages of each should he buy to have the same number of hot dogs and buns?
::Arjay正在计划烧烤。他正在商店买热狗和热狗面包。热狗在8号包里,面包在6号包里。至少每人要买多少个包,才能有同样数量的热狗和面包?

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In this concept, you will learn to find the least   of numbers by using lists.
::在此概念中,您可以通过使用列表来学习如何找到最小的数字 。

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Finding the Least Common Multiple Using Lists
::查找最小通用多用途名单

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Common multiples  are multiples that two or more numbers have in common. The  least common multiple  (LCM) is the smallest  multiple  that two numbers have in common.
::常见倍数是两个或两个以上数字共有的倍数。最小常见倍数(LCM)是两个数字共有的最小倍数。

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Let’s look back at the common multiples for 3 and 4.
::让我们回顾一下3和4的常见倍数。

3, 6, 9,  12 , 15, 18, 21,  24 , 27, 30, 33,  36

4, 8,  12 , 16, 20,  24 , 28, 32,  36 , 40, 44, 48

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Some of the common multiples of 3 and 4 are 12, 24 and 36. The  LCM  of these two numbers is 12. It is the smallest number that they both have in common.
::3号和4号的常见乘数中,有些是12号、24号和36号,这两个数字的LCM是12号,这是它们共有的最小的数字。

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To find the LCM, list the multiples of the two numbers. Stop when you have found the first  common multiple .
::要找到 LCM, 请列出两个数字的多个。 找到第一个常见的多个时停止 。

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Examples
::实例

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Example 1
::例1

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Earlier, you were given a problem about Arjay on his shopping trip.
::早些时候,你在Arjay的购物旅行中 遇到一个问题

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Arjay wants to know at least how many packages of 8 hot dogs and 6 hot dog buns he needs to buy to get the same  amount  of each. Find the LCM of 8 and 6 to find the number of packages for each.
::Arjay想知道至少他要买多少套8个热狗和6个热狗包才能买到每套8个热狗和6个热狗包。 找到8个和6个的LCM来找到每个包的数量。

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First, list the multiples of both 8 and 6. Stop at the first common multiple.
::首先,列出8和6的倍数。 停止在第一个常见的倍数。

8 = 8, 16,  24 , 32

6 = 6, 12, 18,  24

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The LCM of 8 and 6 is 24.
::8和6的LCM为24。

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Then, find number of packages of hot dogs and buns needed to make 24 hotdogs.
::然后,找到做24只热狗所需的热狗和面包包的数量。

$\begin{array}{r}24÷8=3\end{array}$

$\begin{array}{r}24÷6=4\end{array}$

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Arjay must buy 3 packages of hotdogs and 4 packages of hotdog buns to get the same number of each.
::Arjay必须买三包热狗和四包热狗包,

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Example 2
::例2

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Find the LCM of 20 and 15.
::查找20和15的LCM。

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First, list out the multiples of both 20 and 15. Stop at the first common multiple.
::首先,列出20和15的倍数。 停止第一个常见倍数 。

20 = 20, 40,  60 , 80, 100

15 = 30, 45,  60

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The LCM of 20 and 15 is 60.
::20个和15个的LCM为60个。

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Example 3
::例3

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Find the LCM of the pair of numbers.
::找到对数字的 LCM。

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5 and 3
::5和3

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First, list the multiples of both 5 and 3. Stop at the first common multiple.
::首先,列出5和3的倍数。 停止第一个常见的倍数 。

5 = 5, 10,  15 , 20, 25

3 = 3 6, 9, 12,  15

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The LCM of 5 and 3 is 15.
::5和3的LCM为15。

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Example 4
::例4

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Find the LCM of the pair of numbers.
::找到对数字的 LCM。

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2 and 6
::2和6

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First, list the multiples of both 2 and 6. Stop at the first common multiple.
::首先,列出2号和6号的倍数。 停止在第一个常见倍数处。

2 = 2, 4,  6 , 8

6 =  6

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The LCM of 2 and 6 is 6.
::2和6的LCM为6。

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Example 5
::例5

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Find the LCM of the pair of numbers.
::找到对数字的 LCM。

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4 and 6
::第四条和第六条

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First, list the multiples of both 4 and 6. Stop at the first common multiple.
::首先,列出4和6的倍数。 停止在第一个常见的倍数。

4 = 4, 8,  12 , 16, 20

6 = 6,  12

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The LCM of 4 and 6 is 12.
::4和6的LCM为12。

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Review
::回顾

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Find the LCM of each pair of numbers.
::找到每一对数字的 LCM。

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1. 3 and 5
   ::3和5
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2. 2 and 3
   ::2和3
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3. 3 and 4
   ::第3和4条和第3和4条
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4. 2 and 6
   ::2和6
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5. 3 and 9
   ::3和9
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6. 5 and 7
   ::5和7
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7. 4 and 12
   ::第四条和第十二条
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8. 5 and 6
   ::第五条和第六条
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9. 10 and 12
   ::第10和12条
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10. 5 and 8
    ::第5和8条

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Review (Answers) 
::回顾(答复)

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Click   to see the answer key or go to the Table of Contents and click on the Answer Key under the 'Other Versions' option.
::单击可查看答题键, 或转到目录中, 单击“ 其他版本” 选项下的答题键 。

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Resources
::资源