LCM Calculator: Least Common Multiple of Two or More Numbers (with Steps)
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The LCM of 12, 18 and 30 is 180. Take every prime from any number with its largest power: 22 × 32 × 5.
The least common multiple (LCM) of 12, 18 and 30 is 180. It is the smallest positive number that every one of them divides evenly.
Prime factorization of each number
| Number | Prime factors | Goes into the LCM |
|---|---|---|
| 12 | 2^2 × 3 | 15 times |
| 18 | 2 × 3^2 | 10 times |
| 30 | 2 × 3 × 5 | 6 times |
Multiples up to the LCM
| Number | Multiples |
|---|---|
| 12 | 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180 |
| 18 | 18, 36, 54, 72, 90, 108, 126, 144, 162, 180 |
| 30 | 30, 60, 90, 120, 150, 180 |
Show the steps
- Prime factorizations: 12 = 2^2 × 3; 18 = 2 × 3^2; 30 = 2 × 3 × 5.
- Take every prime that appears in any number, with its largest power: 2^2 × 3^2 × 5 = 180.
Least common multiple
LCM(a, b) = a × b ÷ GCF(a, b)
LCM(a, b, c) = LCM(LCM(a, b), c)
- The LCM is the same as the least common denominator when you add fractions whose denominators are these numbers.
Estimates for planning and learning, not financial, tax, legal or medical advice. Check figures with your lender, tax preparer or doctor before you act.
About this calculator
The least common multiple (LCM) of some numbers is the smallest positive number that all of them divide evenly. You need it to add and subtract fractions with different denominators, to find when repeating events line up, and to solve many word problems.
Type your numbers separated by commas or spaces. The calculator shows the LCM, the prime factorization of every number, and how many times each number goes into the LCM. For small answers it also lists the multiples so you can see where they first meet.
How to use it
- Type two or more whole numbers, separated by commas or spaces.
- Read the LCM in the green box and check the prime factor table.
- Open Show the steps to see the method and a check with the GCF.
Three ways to find the LCM
List multiples. Write the multiples of each number until one appears in every list. For 4 and 6: 4, 8, 12 and 6, 12, so the LCM is 12.
Prime factorization. Factor each number. Take every prime that shows up, with its largest exponent, and multiply. For 12 = 22 × 3 and 18 = 2 × 32, the LCM is 22 × 32 = 36.
Use the GCF. For two numbers, LCM = (a × b) ÷ GCF. With 12 and 18 the GCF is 6, so the LCM is 216 ÷ 6 = 36. Try the GCF calculator.
LCM and fractions
The least common denominator of two fractions is the LCM of their denominators. For 1/4 + 1/6 you rewrite both over 12.
Sources
Quick check: test yourself
What is the LCM of 4 and 10?
Correct answer: 20. List the multiples or use LCM = a × b ÷ GCF. Here that is 20.
Which is always true of the LCM of two numbers?
Correct answer: It is a multiple of both. The LCM is the smallest positive number that both divide.
LCM(4, 6) × GCF(4, 6) equals…
Correct answer: 24. For two numbers, LCM × GCF = a × b = 4 × 6 = 24.
Pick an answer for each question.
Common questions
What is the LCM of two numbers?
It is the smallest positive number that both numbers divide evenly. For 4 and 6 it is 12.
How do I find the LCM of three numbers?
Find the LCM of two of them, then the LCM of that answer and the third. Or take every prime from any number with its largest exponent.
What is the LCM of two prime numbers?
Their product, because they share no factor. The LCM of 7 and 13 is 91.
Is the LCM always bigger than the numbers?
It is at least as big as the largest number. It equals the largest number when the others divide it, as with 3 and 12.
What is the difference between LCM and GCF?
The LCM is the smallest shared multiple. The GCF is the largest shared factor. For two numbers, LCM × GCF = a × b.
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