LCM Calculator
The least common multiple is the smallest number that all your numbers divide into exactly. You need it to add fractions with different denominators and to solve “when will they next happen together?” problems.
Answer
LCM(12, 18, 30)
Step by step
- Write each number as a product of primes:
- 12 = 2² × 3
- 18 = 2 × 3²
- 30 = 2 × 3 × 5
- Take every prime that appears, each to its highest power: 2² × 3² × 5.
- Multiply: LCM = 180.
Answer: 180
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How it works
product of each prime at its highest powerLCM(a, b) = a × b ÷ GCF(a, b)List multiples of each number until you find one they share — fine for small numbers.
For bigger numbers use prime factorization: break each number into primes, then take every prime at the highest power it appears in any of them.
For two numbers there is a shortcut: multiply them and divide by their GCF.
Worked example
Find the LCM of 12, 18 and 30.
- 12 = 2² × 3 · 18 = 2 × 3² · 30 = 2 × 3 × 5
- Highest powers: 2² × 3² × 5
- LCM = 180
Frequently asked questions
What is the LCM of 4 and 6?
12. Multiples of 4 are 4, 8, 12…; multiples of 6 are 6, 12…; the first shared one is 12.
What is the difference between LCM and GCF?
The LCM is the smallest number both divide into; the GCF is the largest number that divides into both. For 12 and 18 the LCM is 36 and the GCF is 6.
Why is the LCM used for fractions?
The LCM of the denominators is the least common denominator, the smallest denominator you can rewrite both fractions with before adding or subtracting.