2B Highest common factor and lowest common multiple

Learning intentions for this section:

• To know the meaning of the terms highest common factor (HCF) and lowest common multiple (LCM)

• To be able to find the highest common factor of two numbers

• To be able to find the lowest common multiple of two numbers

Past, present and future learning:

• The concepts in this section may be new to students

• This section prepares students for future work with fractions and other important concepts

• Expertise with these concepts may be required in non-calculator examinations such as NAPLAN and industry aptitude tests

In the previous exercise, factors and multiples of a number were explained. Remember that factors are less than or equal to a given number and that multiples are greater than or equal to a given number.

There are many applications in Mathematics for which the highest common factor (HCF) of two or more numbers must be determined. In particular, the skill of finding the HCF is required for the future topic of factorisation, which is an important aspect of Algebra.

Similarly, there are many occasions for which the lowest common multiple (LCM) of two or more numbers must be determined. Adding and subtracting fractions with different denominators requires the skill of finding the LCM.

People use HCF when calculating equivalent application rates, such as: pool owners simplifying a manufacturer’s chlorine application rates; farmers calculating equivalent fertiliser rates; and nurses and chemists evaluating equivalent medication rates.