LCM Calculator (Least Common Multiple)

Least common multiple of two or more numbers, with steps.

The LCM is the smallest number that all the numbers divide into evenly. LCM(4, 6) = 12: 4 = 2² and 6 = 2 × 3, so take every prime at its highest power, 2² × 3 = 12.

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How to use it

1. Enter two or more whole numbers separated by commas.
2. Read the LCM and the GCF.
3. Check the prime factorization table to see the steps.

What you enter

• Two or more whole numbers

What you get

• Least common multiple
• Greatest common factor
• Prime factorizations

Formula

LCM = product of all primes at their highest powers | LCM(a, b) = a × b ÷ GCF(a, b)

Worked example

Input: 4, 6

Result: LCM = 12

1/4 + 1/6 = 3/12 + 2/12 = 5/12.

Questions

How do you find the least common multiple?

Factor each number into primes and multiply every prime that appears, using its highest power. For two numbers you can also use LCM = a × b ÷ GCF.

What is the LCM used for?

Adding fractions with different denominators (the least common denominator), and timing problems such as when two repeating events next coincide.

What is the LCM of two coprime numbers?

Their product. LCM(8, 9) = 72 because they share no prime factors.

Is the LCM always larger than the GCF?

It is at least as large as the biggest number, and equal to the GCF only when all the numbers are the same.

Limitations

• Whole numbers only; very large lists can give very large LCMs.

References

• Hardy GH, Wright EM, An Introduction to the Theory of Numbers (2008), 6th ed. Oxford University Press.

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All free tools · By Dr. Zubair Khalid, DVM, MS, PhD.