# Maths Topic 08 - Highest common factors and lowest common multiples

Finding the Highest Common Factors and Lowest Common Multiples are maths skills that are commonly tested in 11+ exams and Selective School exams in the UK.

## Examples:

### Example Question 1:

What is the HCF (highest common factor) of 24, 42 and 48?

Explanation: The factors of 24 are: 1, 2, 3, 4, 6, 8, 12 & 24. The factors of 42 are: 1, 2, 3, 6, 7, 14, 21 and 42. The factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48. The highest factor that is common to all numbers is 6.

### Example Question 2:

What is the LCM (lowest common multiple) of 4, 6 and 9?

Explanation: It is best to work on the largest number first, identifying the multiples of 9 and then asking yourself if they are also multiples of 4 and 6.

The multiples of 9 are: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, → . Of these numbers 36 is the lowest multiple that is also common to the numbers 4 and 6 as 36 = 4 × 9 and 36 = 6 × 6. (There are other larger multiples that are common to 4, 6 & 9 e.g. 72, but they are not the LCM.)