Lowest Common Multiple (LCM) and Highest Common Factor (HCF) of Whole Numbers  

 

Welcome to class! 

In today’s class, we will be talking about the lowest common multiple (LCM) and the highest common factor (HCF) of whole numbers. Enjoy the class!

Lowest Common Multiple (LCM) and Highest Common Factor (HCF) of Whole Numbers  

Lowest Common Multiple (LCM) and Highest Common Factor (HCF) of Whole Numbers   classnotes.ng

  • Highest common factor (H.C.F):

The highest common factor of the two given numbers is the highest of the factors common to both numbers.

Example 1

Find the H.C.F. of 20 and 32.

20 = 2 x 2 x 5

32 = 2 x 2 x 2 x 2 x 2

The H.C.E of 20 and 32 is the product of the prime factors common to both numbers.

That is 2 X 2 = 4

Example 2

Find the H.C.F. of 42 and 70.

42 = 2 x 3 x 7

70 = 2 x 5 x 7

The H.C.F. of 42 and 70 = 2 x 7 = 14

Example 3

Find the H.C.F of 2³ x 3² x 5², 2⁴ x 3 x 5³, 3³ x 5 x 7, 2² x 3³ x 5 x 7

2³ x 3² x 5² = 2 x 2 x 2 x 3 x 3 x 5 x 5

2⁴ x 3 x 5³ = 2 x 2 x 2 x 2 x 3 x 5 x 5 x 5

2² x 3³ x 5 x 7 = 3 x 3 x 3 x 5 x 7

H.C.F =3 x 5 = 15

Activity 1

Find the H.C.F of the following:

  1. 60 and 48,
  2. 38 and 95,
  • 60 and 96, by:

(a) the method of listing common factors;

(b) the method of expressing the numbers as products of prime factors. Which of the two methods are less laborious?

Multiples of a Given Whole Number

The 1st multiple of number 7 is 1 X 7 = 7

The 3rd multiple of number 7 is 3 x 7 = 21

The 6th multiple of number 7 is 6 x 7 = 42

The 11th multiple of number 7 is 11 x 7 = 77

The multiple of number 7 may now be listed as 1 x 7, 2 x 7, 3 x 7, 4 x 7…

Note: The three dots… are used to indicate that some multiples in the list have not to be written down. The dots… may be read and so on.

If we list the first six counting numbers, we get, 1, 2, 3, 4, 5, 6. If we multiply each of them by any number, say 7 we get

1 x 7 = 7                 2 x 7 = 14

3 x 7 = 21               4 X 7 = 28

5 x 7 = 35               6 x 7 = 42

We say the numbers 7, 14, 21, 28, 35, 42, are multiples of 7.

Activity 2

Complete the following table

Number

 

Order of Multiple

 

Multiple Number

Required

 

23 8th

 

15

 

12th

 

6 42nd

 

320

 

5th

 

18

 

50th

 

  1. List the first thirty-one multiples of 9 omitting those from the 4th to the 29th.
  2. List the first twenty multiples of 6.
  3. What is the 10th multiple of 12?
  4. List the multiples of 8. How many?
  5. What is the 25th multiple of 24?
  6. What is the 60th multiple of 19?

 

In our next class, we will be talking more about the Lowest Common Multiple (Lcm) and Highest Common Factor (HCF) of Whole Numbers.  We hope you enjoyed the class.

Should you have any further question, feel free to ask in the comment section below and trust us to respond as soon as possible.

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