LCM calculator — lowest common multiple
Enter two or more numbers and the calculator finds their lowest common multiple. Beside the answer it shows the HCF and the prime factorisation.
The LCM of 12, 18, 24 is 72.
Formula
The LCM follows from the HCF: the product of the numbers divided by their highest common factor.
How we got there
For coprime numbers the LCM is just the product, because their HCF is 1.
How to find the LCM by hand
- Find the HCF of the two numbers
For 12 and 18 the highest common factor is 6.
- Multiply the numbers together
12 × 18 = 216.
- Divide the product by the HCF
216 ÷ 6 = 36. That is the lowest common multiple.
- For more numbers, work in pairs
LCM(12, 18, 24) is LCM(LCM(12, 18), 24), that is LCM(36, 24) = 72.
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Frequently asked questions
Divide the product of the numbers by their HCF. For 12 and 18: (12 × 18) ÷ 6 = 36.
For putting fractions over a common denominator, and for questions about events that repeat at different intervals.
Yes, when the numbers are coprime. For 8 and 15 the LCM is 120, exactly their product.
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