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Find the Least Common Multiple (LCM) of 24 and 36 using the prime factors method.

Solution

Find the primes of 24 and 36.
Match primes vertically when possible.

Bring down all columns.
.
Multiply the factors. .
The LCM of 24 and 36 is 72.
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Find the LCM using the prime factors method: 21 and 28.

84

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Find the LCM using the prime factors method: 24 and 32.

96

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Access this online resource for additional instruction and practice with using whole numbers. You will need to enable Java in your web browser to use the application.

Key concepts

  • Place Value as in [link] .
  • Name a Whole Number in Words
    1. Start at the left and name the number in each period, followed by the period name.
    2. Put commas in the number to separate the periods.
    3. Do not name the ones period.
  • Write a Whole Number Using Digits
    1. Identify the words that indicate periods. (Remember the ones period is never named.)
    2. Draw 3 blanks to indicate the number of places needed in each period. Separate the periods by commas.
    3. Name the number in each period and place the digits in the correct place value position.
  • Round Whole Numbers
    1. Locate the given place value and mark it with an arrow. All digits to the left of the arrow do not change.
    2. Underline the digit to the right of the given place value.
    3. Is this digit greater than or equal to 5?
      • Yes—add 1 to the digit in the given place value.
      • No—do not change the digit in the given place value.
    4. Replace all digits to the right of the given place value with zeros.
  • Divisibility Tests: A number is divisible by:
    • 2 if the last digit is 0, 2, 4, 6, or 8.
    • 3 if the sum of the digits is divisible by 3.
    • 5 if the last digit is 5 or 0.
    • 6 if it is divisible by both 2 and 3.
    • 10 if it ends with 0.
  • Find the Prime Factorization of a Composite Number
    1. Find two factors whose product is the given number, and use these numbers to create two branches.
    2. If a factor is prime, that branch is complete. Circle the prime, like a bud on the tree.
    3. If a factor is not prime, write it as the product of two factors and continue the process.
    4. Write the composite number as the product of all the circled primes.
  • Find the Least Common Multiple by Listing Multiples
    1. List several multiples of each number.
    2. Look for the smallest number that appears on both lists.
    3. This number is the LCM.
  • Find the Least Common Multiple Using the Prime Factors Method
    1. Write each number as a product of primes.
    2. List the primes of each number. Match primes vertically when possible.
    3. Bring down the columns.
    4. Multiply the factors.

Practice makes perfect

Use Place Value with Whole Numbers

In the following exercises, find the place value of each digit in the given numbers.

51,493
1
4
9
5
3

thousands hundreds tens ten thousands ones

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87,210
2
8
0
7
1

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164,285
5
6
1
8
2

ones ten thousands hundred thousands tens hundreds

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395,076
5
3
7
0
9

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93,285,170
9
8
7
5
3

ten millions ten thousands tens thousands millions

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36,084,215
8
6
5
4
3

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7,284,915,860,132
7
4
5
3
0

trillions billions millions tens thousands

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2,850,361,159,433
9
8
6
4
2

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In the following exercises, name each number using words.

1,078

one thousand, seventy-eight

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Questions & Answers

A veterinarian is enclosing a rectangular outdoor running area against his building for the dogs he cares for. He needs to maximize the area using 100 feet of fencing. The quadratic equation A=x(100−2x) gives the area, A , of the dog run for the length, x , of the building that will border the dog run. Find the length of the building that should border the dog run to give the maximum area, and then find the maximum area of the dog run.
Elizabeth Reply
ggfcc
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Washing his dad’s car alone, eight year old Levi takes 2.5 hours. If his dad helps him, then it takes 1 hour. How long does it take the Levi’s dad to wash the car by himself?
Gagan Reply
1,75hrs
Mike
I'm going to guess. Divide Levi's time by 2. Then divide 1 hour by 2. 1.25 + 0.5 = 1.3?
John
Oops I mean 1.75
John
I'm guessing this because since I have divide 1 hour by 2, I have to do the same for the 2.5 hours it takes Levi by himself.
John
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Carol
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Jackie
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adeyemi Reply
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Melissa
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Cesarp
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Sunnyshay Reply
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Anton
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Sophia Reply
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Debra
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Cesar
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74.25 × .16 then get the total and that will be your tip
David
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ericka
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David
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Source:  OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
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