Week 9 – Jss 1 First Term General Mathematics Lesson Notes

WEEK 9        L.C.M AND H.C.F (LOWEST AND HIGHEST COMMON FACTOR)
COMMON MULTIPLES AND FACTOR

A prime number is a number that can only divide itself. it has two factor which is 1 and itself. Examples of prime numbers are: 2 ,3, 5, 7, 11, 13, 17, 19 etc.
Multiples: A multiple of a number is obtained by multiplying it by any whole number. Example the multiple of 4 are 4, 8, 12, 16, 20 , 24 etc.
Factors: The factor of a number is the whole number that divides the number exactly.
Example 1: (a) find all the factors of 18
    (b) State which of these factors are even
    ( c) state which of these factors are prime numbers
    (d) Write the first three multiple of 18
Solution

Factors of 18 are 1, 2, 3, 6, 9, and 18
The even numbers are 2, 6, and 18
The prime numbers are 2 and 3

Example 2: Find the factor pairs of 56
Solution:
1 × 56
2 × 28
4 × 14
7 × 8
Therefore the factors of 56 are; 1, 2, 4, 7, 8, 14, 28, and 56.
Product of a Prime Factor
A prime factor is a factor that is also a prime number. You can find the product of prime factors of a number using a prime factor tree method or using the method of dividing repeatedly by the prime numbers.
Example 2: Express the following numbers, 56 and 108, as products of prime factors in index form.
Solution:
Method 1: dividing repeatedly by using prime numbers
2    56                        2    108
2    28                        2    54
2    14                        3    27
7    7                        3    9
    1        Index form = 2³ x 7        3    3
                                1    index form = 2² x 3²
Method 2: Factor tree
        56                    108
    2        28            2        54
        2        14            2        27
            2        7            3        9
                                    3        3

Note that the numbers must be a prime numbers
EXAMPLE 1: Find the L C M of 18 and 24
Solution:
METHOD 1                        METHOD 2
2    18    24                    18 = 2 ×3 ×3
2    9    12                    24 = 2 ×2 ×2 ×3
2    9    6                    L C M = 2 ×2 ×2 ×3 ×3
3    9    3                        = 72
3    3    1
    1    1
L C M = 2 × 2 × 2 × 3 × 3 = 72
Example 2: Find the L C M of 72 and 90
Solution:
METHOD 1                    METHOD 2
2    72    90                72 = 2 X 2X 2 X 3 X 3
2    36    45                90 = 2X 3 X3 X 5
2    18    45                L C M = 2 X 2 X 2 X 3 X 3 X 5
3    9    45                    = 360
3    3    15
5    1    5
    1    1
2 x 2 x 2 x3 x 3 x 5 = 360
Example 3: Find the H C F of 72 and 96
Solution: find the prime product of the number and pick the common ones
72 = 2 * 2 * 2 * 3 * 3
96 = 2 * 2 * 2 * 2 * 2 * 3
H C F = 2 * 2 * 2 * 3 = 24
DO THESE:
EXERCISE 4.2; NO 8, 10, 11, 12 AND 18. PAGE 29
EX 4.5; N0 2 (K L M). PAGE 32