Chapter 8.1, Problem 30HP

To determine

The difference between GCF and LCM of two numbers.

Explanation of Solution

The GCF or the Greatest Common Factor of the two numbers is the largest number that will divide into both of the given numbers. It can be said that GCF is the number which contains all the factors common to both the numbers.

For example:

GCF of 10 and 20 will be:

  $\begin{array}{l}10:1,2,5,10\\ 20:1,2,4,5,10,20\\ \text{Common Pairs:1,2,5,10}\\ \text{Greatest Pair:10}\\ \text{GCF=10}\end{array}$

The LCM or the Least Common Multiple of two numbers is the smallest number that both the numbers divide into. It can be said that LCM of two numbers contains both the numbers as factors and this smallest number is the common multiple of those two numbers.

For example:

LCM of 6 and 12 will be:

  $\begin{array}{l}\text{Multiples of 6 and 12:}\\ 6:6,12,18,24,30,36,42,48,54,60\\ 12:12,24,36,48,60\\ \text{Common Pairs:12,24,36,48,60}\\ \text{Smallest Pair:12}\\ \text{LCM=12}\end{array}$