Page 39 - Mathematics of Business and Finance

Chapter 1 | Review of Basic Arithmetic 19

Solution Method 2
continued
1 16 20
4 × 4 4 × 5
2 × 2 × 2 × 2 2 × 2 × 5

2 Number of 2's = 2
Number of 2's = 4
Number of 5's = 1
3 Largest count for the prime number 2 = 4
Largest count for the prime number 5 = 1
4 LCM = 2 × 2 × 2 × 2 × 5 = 80

Therefore, the two flashing lights will flash together every 80 seconds.

Least or Lowest Common Denominator (LCD)

The Least Common Denominator (LCD) of a set of two or more fractions is the smallest whole
number that is divisible by each of the denominators. It is the least common multiple (LCM) of the
denominators of the fractions.
In performing the addition and subtraction of fractions, it is necessary to determine the equivalent
fraction using the least common denominator. The best choice for a common denominator is the LCD,
because it makes any further simplification easier.

Example 1.2(g) Determining the Least Common Denominator
4 7
Determine the LCD of and .
9 15

Solution 4 7
The LCD of the fractions and is the same as the LCM of the denominators 9 and 15. It is the
9 15
4 7
same as in Example 1.2(e)(iii). Therefore, the LCD of and is 45.
9 15

Greatest Common Factor (GCF)

The factors that are common to two or more numbers are called common factors of those numbers.
The GCF is the largest
integer that divides the
set of numbers The Greatest Common Factor (GCF) of two or more numbers is the largest common number that
with no remainder. divides the numbers with no remainder. In other words, the GCF is the largest of all the common
factors.

Example 1.2(h) Determining the Greatest Common Factor
Determine the greatest common factor of 12 and 18.

Solution Method 1
First list all the factors of all the numbers. Then select all the common factors of the numbers. The
highest value of the common factors is the greater common factor (GCF).