LCM Calculator
Get the smallest number that every number in your list divides evenly.
How to use the LCM Calculator
- Enter the whole numbers.
- Press Calculate. The result updates automatically as you type.
About the LCM Calculator
The least common multiple is the smallest positive number that is a multiple of every number in a set. Its most familiar job is finding the least common denominator when adding fractions such as 1/12 + 1/18. It also answers timing questions: if one bus comes every 12 minutes and another every 18, they arrive together every 36 minutes.
Listing multiples works for small numbers but gets slow quickly. Prime factorization is faster and shows why the answer is right: the LCM must contain every prime factor of every number, at the highest power any of them uses. The GCF shown alongside uses the lowest powers instead. For any two numbers, LCM × GCF equals their product.
Formula
LCM = product of each prime raised to its highest power in any of the numbers
For 12 = 2² × 3, 18 = 2 × 3² and 30 = 2 × 3 × 5, the LCM is 2² × 3² × 5 = 180. For two numbers there is also a shortcut: LCM(a, b) = a × b ÷ GCF(a, b).
Example calculation
Using the default values:
- Whole numbers = 12, 18, 30
the calculator returns:
- Least common multiple: 180
- Greatest common factor: 6
- LCM from highest powers: 2^2 × 3^2 × 5 = 180
Frequently asked questions
What is the LCM of 4 and 6?
12. The multiples of 4 are 4, 8, 12… and of 6 are 6, 12…, so 12 is the first one they share.
How is the LCM used with fractions?
The LCM of the denominators is the least common denominator. To add 1/4 + 1/6, rewrite both over 12: 3/12 + 2/12 = 5/12.
What is the difference between LCM and GCF?
The LCM is the smallest number all the numbers divide into; the GCF is the largest number that divides all of them.
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