HCFs and LCMs

You will Learn to:

    - Fnd the HCF and LCM of two numbers

HCF

The Highest Common Factor is the largest whole number that will divide into both numbers without leaving a remainder.

Worked example.

        Find the HCF of 196 and 420

1. List both numbers’ prime factors 196 = 2 X 2 X 7 X 7 420 = 2 X 2 X 3 X 5 X 7
2. Match up all the pairs. 196 = {2} X [2] X (7) X 7 420 = {2} X [2] X (7) X 3 X 5

3. Multiply together one from each pair. 2 X 2 X 7 = 28

        The HCF of 196 and 420 = 28
   

LCM

    The LCM of two numbers is the lowest multiple of both of the numbers.

Worked Example

    Find the LCM of 96 and 120

1. Write the numbers and products of their primes.

     96 = 2 X 2 X 2 X 2 X 2 X 3
   120 = 2 X 2 X 2 X 3 X 5
   

2. Again, Find the pairs.

     96 = (2) X [2] X {2} X <3> X 2 X 2
   120 = (2) X [2] X {2} X <3> X 5
   

3. Instead of just multiplying together one from each pair, multiply togetether one from each pair and whatevers left.

    LCM(96, 120) = 2 X 2 X 2 X 3 X 2 X 2 X 5
                        = 2 X 2 X 2 X 2 X 2 X 3 X 5
                        = 2 <sup>5</sup> * 15
                        = 480