LCM Calculator · Practical guide
What Is the LCM of 12 and 18?
The LCM of 12 and 18 is 36 — the smallest number both 12 and 18 divide into evenly.
At a glance
The Answer
lcm(12, 18) = 36. The multiples of 12 are 12, 24, 36, 48... and the multiples of 18 are 18, 36, 54... — the first match is 36. Enter "12, 18" in the calculator above to confirm it and see the working.
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Enter your own values, then compare the result with the examples below.
Results
Method 1: The GCD Formula
The formula is lcm(a, b) = |a x b| / gcd(a, b). The greatest common divisor of 12 and 18 is 6 (both divide evenly by 6, and nothing larger). So:
lcm(12, 18) = 12 x 18 / 6 = 216 / 6 = 36
Method 2: Prime Factorization
Break each number into primes and take each prime at its highest power:
- 12 = 2 x 2 x 3 (that is 2^2 x 3)
- 18 = 2 x 3 x 3 (that is 2 x 3^2)
- Highest powers: 2^2 x 3^2 = 4 x 9 = 36
The calculator shows these factorizations alongside the result, so you can check your homework step by step.
Common LCM Pairs for Reference
| Pair | GCD | LCM |
|---|---|---|
| 4 and 6 | 2 | 12 |
| 8 and 12 | 4 | 24 |
| 12 and 18 | 6 | 36 |
| 10 and 15 | 5 | 30 |
| 14 and 21 | 7 | 42 |
| 16 and 24 | 8 | 48 |
Spot the Pattern
Notice that gcd x lcm = a x b for any pair. For 12 and 18: 6 x 36 = 216 = 12 x 18. That identity is a fast way to check your answer — if the product of your gcd and lcm does not equal the product of the two numbers, something went wrong.
Frequently Asked Questions
What is the GCF of 12 and 18?
The greatest common factor is 6. The shared factors of 12 and 18 are 1, 2, 3, and 6, and 6 is the largest.
Is 36 the only common multiple of 12 and 18?
No — 72, 108, and every multiple of 36 are also common multiples. Thirty-six is simply the least of them, which is what LCM means.
Why is the LCM not just 12 times 18?
Multiplying gives 216, which counts the shared factor 6 twice. Dividing by the gcd removes the double count: 216 / 6 = 36.
What is the LCM of 12, 18, and 24?
It is 72. First lcm(12, 18) = 36, then lcm(36, 24) = 72. You can verify all three at once by entering "12, 18, 24" above.