# HCF and LCM

The highest common factor (HCF) is the biggest number that divides into both numbers. The lowest common multiple (LCM) is the smallest number both go into.

Maths (school) · Part 01: Number and ratio · Card 9 of 9 · Last updated 2026-10-19

## Analogy

HCF is the biggest tile that fits both floors. LCM is when two buses next meet at the stop.

## Example

**36 and 60**

36 = 2^2 x 3^2
60 = 2^2 x 3 x 5
HCF = 2^2 x 3 = 12
LCM = 2^2 x 3^2 x 5 = 180

## In practice

Two buses leaving every 12 and 15 minutes line up again after 60 minutes, the LCM.

## Practice

### Flashcards

- **What is the HCF of 36 and 60?** 12. It is the biggest number that divides into both.

### Interview questions

**Write 36 and 60 as products of prime factors, then find their HCF and LCM.**

- 36 = 2^2 x 3^2
- 60 = 2^2 x 3 x 5
- HCF uses shared primes with smaller powers: 12
- LCM uses every prime with larger powers: 180

## Questions people ask

### How do you find the HCF using prime factors?

Write each number as a product of primes, then multiply the primes they share, using the smaller power each time. For 36 = 2^2 x 3^2 and 60 = 2^2 x 3 x 5, the shared part is 2^2 x 3 = 12.

### What is the difference between a factor and a multiple?

A factor divides exactly into a number: the factors of 12 include 3 and 4. A multiple is in that number's times table: the multiples of 12 include 24 and 36. Factors are small or equal, multiples are big or equal.

## Related concepts

- [BIDMAS](https://studyvisually.com/learn/science/maths-school/maths-school-part-1/maths-school-part-1-concept-1)
- [Adding fractions](https://studyvisually.com/learn/science/maths-school/maths-school-part-1/maths-school-part-1-concept-2)
- [Percentage of an amount](https://studyvisually.com/learn/science/maths-school/maths-school-part-1/maths-school-part-1-concept-3)
- [Percentage change](https://studyvisually.com/learn/science/maths-school/maths-school-part-1/maths-school-part-1-concept-4)

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