HCF and LCM calculator
HCF and LCM of 72, 120
HCF 24 · LCM 360
The highest common factor is 24 and the lowest common multiple is 360.
- 72
- 2³ × 3²
- 120
- 2³ × 3 × 5
Working
- 72 = 2³ × 3².
- 120 = 2³ × 3 × 5.
- HCF: take each prime that is in every number, with its lowest power: 2³ × 3 = 24.
- LCM: take every prime, with its highest power: 2³ × 3² × 5 = 360.
- Check: HCF × LCM = 24 × 360 = 8,640 = 72 × 120.
Your result
HCF 24 · LCM 360. The highest common factor is 24 and the lowest common multiple is 360.
Primes, HCF and LCM
GCSE Maths Pro
Get a grade 8 or your money back
£119 once
No VAT is charged. Conditions
Your mock plan, in three taps
HCF and LCM from prime factors: 72 = 2³ × 3² and 120 = 2³ × 3 × 5, so the HCF is 2³ × 3 = 24 and the LCM is 2³ × 3² × 5 = 360.
Questions people ask
How do you find the HCF using prime factors?
Write both numbers as products of primes and multiply the primes they share, each to the lower power. 84 = 2² × 3 × 7 and 90 = 2 × 3² × 5 share 2 and 3, so the HCF is 2 × 3 = 6.
How do you find the LCM using prime factors?
Multiply every prime that appears in either number, each to the higher power. For 84 and 90: 2² × 3² × 5 × 7 = 1,260.
How do you use a Venn diagram for HCF and LCM?
Put the shared prime factors in the overlap and the rest in each circle. The HCF is the product of the overlap; the LCM is the product of everything in the diagram.
What is a quick check?
For two numbers, HCF × LCM equals the two numbers multiplied together: 6 × 1,260 = 84 × 90 = 7,560.
More free tools
Keep going
How we work this out
What it does
Type two to four numbers to find their highest common factor and lowest common multiple from their prime factors.
2 to 4 whole numbers from 1 to 10,000,000.
Method
- Write each number as a product of prime factors in index form.
- HCF: multiply the primes that are in every number, each at its lowest power.
- LCM: multiply every prime that appears, each at its highest power.