LCM Calculator · Practical guide
How to Find the LCM of 3 Numbers
Work in pairs: find the LCM of two numbers, then combine that result with the third.
At a glance
The Short Answer
To find the LCM of 3 numbers, apply the two-number formula twice: first lcm(a, b), then lcm(that result, c). For example, lcm(4, 6) = 12, and lcm(12, 8) = 24, so lcm(4, 6, 8) = 24. The calculator above does the chaining for you — just enter the numbers separated by commas.
Interactive tool
LCM Calculator
Enter your own values, then compare the result with the examples below.
Results
The Formula, Step by Step
For any two numbers, lcm(a, b) = |a x b| / gcd(a, b), where gcd is the greatest common divisor. Extending to three numbers:
- Find gcd(4, 6) = 2, so lcm(4, 6) = 24 / 2 = 12.
- Find gcd(12, 8) = 4, so lcm(12, 8) = 96 / 4 = 24.
- Answer: lcm(4, 6, 8) = 24.
Prime Factorization Method
You can also take each prime at its highest power across all numbers. For 4, 6, 8: the primes are 2 and 3; the highest power of 2 is 2^3 (from 8) and of 3 is 3^1 (from 6), so LCM = 8 x 3 = 24. Both methods always agree.
Quick Reference Table
| Numbers | LCM |
|---|---|
| 4, 6, 8 | 24 |
| 6, 8, 9 | 72 |
| 12, 15, 20 | 60 |
| 3, 5, 7 | 105 |
A Common Mistake
Multiplying all three numbers only works when they share no factors at all. 3 x 5 x 7 = 105 happens to be correct because the numbers are coprime, but 4 x 6 x 8 = 192 is eight times the true LCM of 24. When in doubt, divide out the shared factors — or let the calculator show you the prime factors it used.
Frequently Asked Questions
Does the order of the numbers matter?
No. LCM is associative, so lcm(lcm(a, b), c) equals lcm(a, lcm(b, c)). You will get the same answer no matter which pair you start with.
Can I enter more than three numbers?
Yes. The same chaining works for any count, and the calculator accepts a comma-separated list of any length.
What if one number is a multiple of the others?
The LCM is simply the largest number. For example, lcm(3, 6, 12) = 12, because 12 is already divisible by 3 and 6.
Can I use negative numbers?
Yes. LCM is defined for positive integers, so the calculator uses absolute values — lcm(-4, 6) is the same as lcm(4, 6) = 12.