Page 36 - Mathematics of Business and Finance

16 Chapter 1 | Review of Basic Arithmetic

Example 1.2(a) Identifying Prime Numbers and Composite Numbers
(i) Identify all the prime numbers less than 25.
(ii) Identify all the composite numbers less than 25.

Solution (i) All the prime numbers less than 25 are: 2, 3, 5, 7, 11, 13, 17, 19, and 23.
(ii) All the composite numbers less than 25 are: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, and 24.

Example 1.2(b) Determining Factors of Prime Numbers
Determine all the factors of 13.

Solution 1 and 13 are the only factors of 13. 1 13

Example 1.2(c) Determining All Factors of Composite Numbers
Determine all the factors of:

(i) 18 (ii) 20

Solution (i) The factors of 18 are: 1, 2, 3, 6, 9, and 18. 1 2 3 6 9 18

(ii) The factors of 20 are: 1, 2, 4, 5, 10, and 20. 1 2 4 5 10 20

Example 1.2(d) Determining Prime Factors of Composite Numbers
Determine the prime factors of 24.

Solution All the factors of 24 are: 1, 2, 3, 4, 6, 8, 12, and 24. 1 2 3 4 6 8 12 24
In the above factors, only 2 and 3 are prime numbers.
Therefore, the prime factors of 24 are: 2 and 3.

Least or Lowest Common Multiple (LCM)

The Least Common Multiple (LCM) of two or more whole numbers is the smallest multiple that is
common to those numbers. The LCM can be determined using one of the following methods:
Method 1

1. First, select the largest number and check to see if it is divisible by all the other numbers. If it
divides, then the largest number is the LCM.

For example, in finding the LCM of 2, 3, and 12, the largest number 12 is divisible by the other
numbers 2 and 3. Therefore, the LCM of 2, 3, and 12 is 12.
2. If none of the numbers have a common factor, then the LCM of the numbers is the product of all
the numbers.
For example, in finding the LCM of 2, 5, and 7, none of these numbers have a common factor.
Therefore, the LCM of 2, 5, and 7 is 2 × 5 × 7 = 70.
3. If the largest number is not divisible by the other numbers and there is a common factor between
some of the numbers, then find a multiple of the largest number that is divisible by all the other
numbers.