LCM calculator with steps (lowest common multiple)

1. Write each number as a product of prime factors, for example $12 = 2^2 \times 3$ and $18 = 2 \times 3^2$.
2. List every prime that appears in any of the numbers.
3. Take each prime with its highest power: $2^2$ and $3^2$.
4. Multiply them: $\text{LCM} = 2^2 \times 3^2 = 36$.

For small numbers you can also list multiples (12, 24, 36, … and 18, 36, …) until one appears in both lists, but prime factors are quicker for large numbers and are what exams usually expect.

• $12 = 2^2 \times 3$
• $18 = 2 \times 3^2$
• $30 = 2 \times 3 \times 5$

Highest powers: $2^2$, $3^2$ and $5$. So the LCM is $4 \times 9 \times 5 = 180$. Check: $180 \div 12 = 15$, $180 \div 18 = 10$ and $180 \div 30 = 6$, all whole numbers.

See our guide on how to find the LCM for more methods and exam-style questions.

• Taking the lowest powers. That gives the HCF, not the LCM.
• Multiplying the numbers together. $12 \times 18 = 216$ is a common multiple, but not the lowest.
• Missing a prime that appears in only one number, like the 5 in 30.

For two numbers, $\text{HCF} \times \text{LCM} =$ the product of the numbers. For 12 and 18: $6 \times 36 = 216 = 12 \times 18$. It's a handy check, but it only works for two numbers. The calculator shows both answers; for the HCF method, see the HCF calculator.