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JSS2: MATHEMATICS - 1ST TERM

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  1. Properties of Whole Numbers I | Week 1
    4 Topics
    |
    1 Quiz
  2. Properties of Whole Numbers II | Week 2
    4 Topics
    |
    1 Quiz
  3. Properties of Whole Numbers III | Week 3
    5 Topics
    |
    1 Quiz
  4. Indices | Week 4
    2 Topics
    |
    1 Quiz
  5. Laws of Indices | Week 5
    5 Topics
    |
    1 Quiz
  6. Whole Numbers & Decimal Numbers | Week 6
    4 Topics
    |
    1 Quiz
  7. Standard Form | Week 7
    3 Topics
    |
    1 Quiz
  8. Significant Figures (S.F) | Week 8
    4 Topics
    |
    1 Quiz
  9. Fractions, Ratios, Proportions & Percentages I | Week 9
    6 Topics
    |
    1 Quiz
  10. Fractions, Ratios, Proportions & Percentages II | Week 10
    4 Topics
    |
    1 Quiz
  11. Fractions, Ratios, Proportions & Percentages III | Week 11
    3 Topics
    |
    1 Quiz
  12. Approximation & Estimation | Week 12
    1 Topic
    |
    1 Quiz
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Topic Content:

  • Meaning of Lowest Common Multiple (LCM)
  • Different Methods of Finding LCM

What is LCM?

The lowest common multiple of two or more numbers is the lowest multiple they have in common. 

For example:

The multiples of 2 are  2, 4, 6, 8, 190, 12, 14, 16, 18……

The multiples of 3 are 3, 6, 9, 12, 15, 18 …….

The common multiples of 2 and 3 are 6, 12, 18, ……

The lowest common multiple of 2 and 3 is 6.

Method 1 (Short Division Method):

LCM by division method means finding the least common multiple of a given set of numbers by dividing all the given numbers by a common prime number.

Method 2 (Prime Factorization Method):

Using this method we find the prime factors of the given numbers. We the select each prime factor with the “highest power” and multiply to get the LCM.

Let’s try some examples.

Worked Example 1.4.1:

Find the LCM of:

a. 3, 7 and 10

b. 9 and 15

c. 2 ,3 and 4

d.
23 × 32 × 5
22 × 3 × 5

e.
24 × 32 × 5 × 7 × 112   
23 × 5 × 73 × 11
22 × 33 × 5 × 72 × 11

a. 3, 7 and 10

Solution

1st Method (Division Method):

Screenshot 2023 08 19 at 16.14.41

Let us understand this method using the example given below.

Step 1: 2 is the smallest prime number and it is a factor of 10. Write 2 on the left of the three numbers. For each number in the right column, continue calculating out prime numbers which are their factors.

Step 2: 2 divides 10 and the result is 5. But 2 is not a factor of 3 and 7, so we write the number 3 and 7 in the row below as it is.

Step 3: We continue the process until we have only 1’s left

Step 4: Our final step is to multiply the prime numbers on the left. The Least Common Multiple (LCM) is the product of all these prime numbers.

LCM  = 2 × 3 × 5 × 7

= 6 × 35

=  210

2nd Method:

Find the prime factors of the given numbers.

Screenshot 2023 08 19 at 16.46.31

3 = 1 × 3
7 = 1 × 7
10 = 2 × 5

Select each prime factor with the “highest power” and multiply to get the LCM.

∴ L.C.M. = 1 × 2 × 3 × 7 × 5

= 210

b. 9 and 15

Solution

1st Method (Division Method):

Screenshot 2024 03 30 at 09.48.12

∴ L.C.M. = 3 × 3 × 5

= 9 × 5

= 45

2nd Method (Prime Factorization Method):

Step 1: Resolve each given number into its prime factors and express the factors obtained in exponent form.

Screenshot 2023 08 20 at 03.29.19

9 = 3 × 3 = 32

15 = 3 × 5

Step 2: Find the product of all the prime factors with highest powers.

= 32 × 5

= 9 × 5

= 45

c. 2, 3 and 4

Solution

Screenshot 2023 08 20 at 00.02.46

LCM of 3 and 4 = 2 × 2 × 3 = 12

d.

23 × 32 × 5
22 × 3 × 5

Solution

In this case, compare the index (power) of numbers with the same base. The numbers with greater power (index) are the common multiple.

23 × 32 × 5

22 × 3 × 5

= 23  ×   32   ×   5

LCM   =   23   ×  32   ×  5

e.

24 × 32 × 5 × 7 × 112 
23 × 5 × 73 × 11
22 × 33 × 5 × 72 × 112

Solution

Screenshot 2023 08 20 at 03.26.09 1

LCM   =   24   ×  33   ×  5  ×  73   ×  112

Evaluation Questions:

1. Find all the factors of 48

View Answer

2. Find the factors of 100 that are

i. Odd numbers
ii. Even numbers
iii. Multiples of 2
iv.  Multiples of 5

View Answers

3. Write down the first six multiples of 7

View Answer

4. Express the following numbers as a product of prime factors.

a. 64
b.  120    
c.  500    
d.   980

View Answers

5. Express  24 × 36  as a product of its prime factors in index form.

View Answer

6. Find the common factors of the following:

a. 16 and 30
b. 36 and 50

View Answers

7. Find the HCF of:

a. 4 and 12
b. 9, 18 and 54
c. 36 and 81

View Answers

8. Find the HCF of

a. 22 × 32 × 53 × 7  and 24 × 35 × 5 × 72

b. 52 × 73  and  53 × 74

View Answers

9. Find the first three common multiples of

a. 5 and 6
b. 2,  3  and 4

View Answers

10. Find the LCM of

a. 12, 18 and 36
b. 5,  10, and 15
c. 52 × 7 × 11,    2 × 3 × 5 × 11
d. 23  × 3  × 53;        2 × 32 ×  52;      23  × 33  ×  5 × 72

View Answers
avatar

All factors of 48 are;

1, 2, 3, 4, 6, 8, 12, 16, 24, and 48

i. Odd numbers – 1, 5, 25

ii. Even numbers – 2, 4, 10, 20, 50 and 100

iii. Multiples of 22, 4,10, 20, 50 and 100

iv. Multiples of 5 – 5, 10, 20, 25, 50 and 100

The first six multiples of 7 are

:-  7, 14, 21, 28, 35, and 42

a. 64 = 2 x 2 x 2 x 2 x 2 x 2 

b. 120 = 2 x 2 x 2 x 3 x 5

c.  500 = 2 x 2 x 5 x 5 x 5

d. 980 = 2 x 2 x 5 x 7 x 7

24 x 36 = 25 x 33

a. Common factors of 16 and 30 = 1,2

b. Common factors of 36 and 50 = 1,2

Find the HCF  of

a. HCF of 4 and 12 = 4

b. HCF of 9, 18 and 54 = 9

c. HCF of 36 and 81 = 9

a. HCF of 22 x 32 x 53 x 7  and 24 x 35 x 5 x 72 = 22 x 32 x 5 x 7 = 1260

b. HCF of  52 x 73  and  53 x 74 = 52 x 73= 8575

a. The first three common multiples of 5 and 6 = 30, 60, 90

b. The first three common multiples of 2, 3, and 4 = 12, 24, 36

a. The LCM of  12, 18 and 36 = 36

b. The LCM of  5,  10, and 15 = 30

c. The LCM of  52 x7 x 11,    2 x 3 x 5  x 11 = 2 x 3 x 52 x 7 x 11

d. The LCM of 

23  x 3  x 53        

2 x 32 x  52     

23  x 33  x  5 x 7

=23 x 3x  53 x 72