How it works

To find the HCF and LCM efficiently, write each number as a product of prime factors, usually shown in a Venn diagram or index form. The HCF is the product of the common prime factors (lowest powers), while the LCM is the product of all prime factors involved (highest powers). This method avoids listing every factor or multiple.

The method

1. 1.Write each number as a product of prime factorsUse a factor tree
2. 2.Place the factors into a Venn diagram or list them in index form
3. 3.HCF = product of factors common to both numbers
4. 4.LCM = product of all factors, using the highest power of each

Worked example

Find the HCF and LCM of 24 and 36.

1. 24 = 2^3 x 3, 36 = 2^2 x 3^2
2. HCF = 2^2 x 3 = 12
3. LCM = 2^3 x 3^2 = 72

Worked example

Find the LCM of 8 and 12.

1. 8 = 2^3, 12 = 2^2 x 3
2. LCM = 2^3 x 3 = 24

Common mistakes

• Confusing HCF with LCM and multiplying the wrong set of factors
• Forgetting to include a prime factor that appears in only one number when finding LCM
• Using the highest power instead of the lowest power when finding HCF