HCF and LCM

In a Nutshell

The HCF is the biggest factor two numbers share; the LCM is the smallest number they both go into.

Start by writing each number as a product of prime factors. A Venn diagram is the clearest way to sort them: shared primes sit in the overlap, the rest stay on their own side.

HCF (Highest Common Factor): multiply together the primes in the overlap.

LCM (Lowest Common Multiple): multiply together all the primes in the diagram (overlap included, but counted only once).

To find the HCF, multiply the prime factors that appear in both numbers. To find the LCM, multiply all the prime factors in the diagram, using each factor the greatest number of times it appears in either number.

Venn diagram showing prime factors for HCF and LCM Two overlapping circles. The left circle holds prime factors unique to the first number, the right circle holds prime factors unique to the second number, and the overlap holds shared prime factors. 12 18 2 2 × 3 3 HCF = 6 LCM = 36

Choose a pair of numbers. The diagram splits the prime factors into three zones: left only, shared, and right only. Multiply the shared primes for the HCF. Multiply every prime you can see for the LCM.

Watch it work

Question: Find the HCF and LCM of 24 and 36.

Have a go

Q1. Find the HCF and LCM of 12 and 18.

Q2. Find the HCF and LCM of 15 and 20.

Q3. Find the HCF and LCM of 8 and 12.

Q4. Two buses leave a bus station at 9:00 am. Bus A returns every 12 minutes and Bus B returns every 18 minutes. When will they next both be at the station at the same time?