How to find the LCM (lowest common multiple): 3 methods

TutorAura guide · Updated 25 October 2026

The lowest common multiple (LCM) of two or more numbers is the smallest number that all of them divide into exactly. The LCM of 4 and 6 is 12: it's in the 4 times table (4, 8, 12) and the 6 times table (6, 12). There are three common methods; prime factors are the most reliable for larger numbers.

Key takeaways

Listing multiples works for small numbers.
Prime factors: take every prime with its highest power.
A Venn diagram shows the HCF and LCM together.
LCM questions often ask when things next happen together.

Method 1: list multiples

List multiples of each number until one appears in every list.

6: 6, 12, 18, 24, 30
8: 8, 16, 24, 32

LCM = 24. Fine for small numbers, slow for large ones.

Method 2: prime factors

Write each number as a product of primes: $24 = 2^3 \times 3$ and $90 = 2 \times 3^2 \times 5$ .
Take every prime that appears, with its highest power: $2^3$ , $3^2$ , $5$ .
Multiply: $8 \times 9 \times 5 = 360$ .

Use our prime factorisation calculator to check factor trees.

Method 3: Venn diagram

Put the prime factors of each number in two overlapping circles, with shared factors in the middle. For 24 ( $2, 2, 2, 3$ ) and 90 ( $2, 3, 3, 5$ ): the middle has $2, 3$ ; 24's side has $2, 2$ ; 90's side has $3, 5$ .

LCM = product of everything: $2 \times 2 \times 2 \times 3 \times 3 \times 5 = 360$ . (HCF = product of the middle: $2 \times 3 = 6$ .)

Word problems

Bus A leaves every 12 minutes and bus B every 20 minutes. They both leave at 9:00. When do they next leave together?

LCM of 12 and 20: $12 = 2^2 \times 3$ , $20 = 2^2 \times 5$ , so LCM $= 2^2 \times 3 \times 5 = 60$ . They leave together again 60 minutes later, at 10:00.

Clue words: "next time together", "smallest number of packs", "fewest".

Common mistakes

Using the lowest powers (that's the HCF).
Multiplying the numbers: $12 \times 20 = 240$ is a common multiple, not the lowest.
Leaving out a prime that's only in one number.

Practice

Find the LCM of: (a) 8 and 12, (b) 15 and 25, (c) 6, 10 and 15. Answers: 24, 75, 30. Check with the LCM calculator, and see how to find the HCF.

The LCM of three numbers

Prime factors work for any number of values. For 4, 6 and 10:

$4 = 2^2$
$6 = 2 \times 3$
$10 = 2 \times 5$

Take each prime with its highest power: $2^2 \times 3 \times 5 = 60$ . Check: $60 \div 4 = 15$ , $60 \div 6 = 10$ , $60 \div 10 = 6$ . All whole numbers, so 60 is a common multiple, and no smaller number works.

LCM and HCF together

For two numbers, the HCF multiplied by the LCM equals the two numbers multiplied together:

\text{HCF} \times \text{LCM} = a \times b

For 12 and 20: HCF $= 4$ , LCM $= 60$ , and $4 \times 60 = 240 = 12 \times 20$ . It's a quick way to check your answers, or to find one if you know the other. (It doesn't work for three or more numbers.)

Using the LCM to add fractions

The lowest common denominator of two fractions is the LCM of their denominators:

\frac{5}{6} + \frac{3}{8} = \frac{20}{24} + \frac{9}{24} = \frac{29}{24} = 1\tfrac{5}{24}

Using 48 ( $6 \times 8$ ) also works, but the numbers are bigger and you'd have to simplify at the end. Try it in the fraction calculator.

Frequently asked questions

Can the LCM be one of the numbers?

Yes. If one number is a multiple of the other, the larger number is the LCM. The LCM of 4 and 12 is 12.

What is the difference between the LCM and the HCF?

The LCM is the smallest number that all the numbers divide into; it is at least as big as the largest number. The HCF is the largest number that divides into all of them; it is at most as big as the smallest number. With prime factors, the LCM uses the highest powers and the HCF the lowest powers of shared primes.

What is the LCM of 6 and 8?

24. Multiples of 6 are 6, 12, 18, 24 and multiples of 8 are 8, 16, 24, so 24 is the first number in both lists. With prime factors: 6 = 2 × 3 and 8 = 2³, so the LCM is 2³ × 3 = 24.

Sources

National curriculum in England: mathematics programmes of study. Department for Education.
Common Core State Standards for Mathematics. Common Core State Standards Initiative.
Mathematics GCSE subject content and assessment objectives. Department for Education.

HCF and LCM questions and answers

8 GCSE and IGCSE questions with worked answers, checked as you type.

LCM calculator with steps (lowest common multiple)

Lowest common multiple of 2 to 10 numbers, with prime factors, a Venn diagram and every step.

How to find the HCF (highest common factor): 3 methods

Listing factors, prime factors and Euclid's method, with worked examples and word problems.

Factor trees: how to find prime factors step by step

How to draw a factor tree, write the answer in index form, and use it for HCF, LCM and roots.

Prime factorisation, HCF and LCM

Write a number as a product of primes with a factor tree, then use it to find the highest common factor and lowest common multiple.