LESSON 4 – MULTIPLES AND LEAST COMMON MULTIPLES

Objectives:

At the end of the lesson, students should be able to;

  • List the multiples of any given number

  • Identify and list the common multiples

  • Pick out the smallest or least number or numbers from the list. This is the lowest common multiple.

 The multiples of a number are those numbers into which that number divides evenly.

Examples 1

List the first 5 multiples of 7.

7 = {7, 14, 21, 28, 35}

List the first 5 multiples of 9

9 = {9, 18, 27, 36, 45}

List the first 5 multiples of 8

8 = {8, 16, 24, 32, 40}

List the first 5 multiples of 12

12={12, 24, 36, 48, 60}

Examples 2

Write down the common multiples of 3 and 4

           First list at least the first 12 multiples of each number.

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

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

           List all the common multiples.

              Common multiples of 3 and 4  = {12, 24, 36}

Examples 3

Write down the common multiples of 5 and 10

5 and 10

5 = {5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60}

10 = {10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120}

CM = {10, 20, 30, 40, 50, 60}

Examples 4

Write down the common multiples of 3 and 9

3 and 9

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

9 = {9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108}

CM = {9, 18, 27, 36}

  • Write down the common multiples of 2, 4 and 8

2, 4 and 8

2 = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28}

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

8 = {8, 16, 24, 32, 40, 48, 56, 64, 72, 72, 80, 88, 96}

C.M = {8, 16, 24}

Note: sometimes you may have to list multiples beyond the first 12.

Find the least common multiples of the following sets of numbers.

  • 3 and 6

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

6 = {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72}

CM = {6, 12, 18, 24, 30, 36}

LCM = {6}

  • 5 and 10

5 = {5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70}

10 = {10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120}

CM = {10, 20, 30, 40, 50, 60, 70}

LCM = {10}

  • 3 and 9

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

9 = {{9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108}

CM = {9, 18, 27, 36}

LCM = {9}

  • 3, 6 and 9

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

6 = {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72}

9 = {9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108}

CM = {18, 36}

LCM = {18}

  • 4, 8 and 12

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

8 = {8, 16, 24, 32, 40, 48, 56, 64, 72, 72, 80, 88, 96}

12 = {12, 24, 36, 48, 60, 72, 84, 84, 96, 108, 120, 132, 144}

CM = {24, 48}

LCM = {24}

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