Classroom Troubleshooting
7 Common LCM Mistakes Students Actually Make
After grading thousands of middle-school and algebra worksheets, you see the exact same seven slips happen over and over. None of them mean you are bad at math—they usually happen when two similar rules get tangled. Here is how to spot and fix each one.
Adding prime exponents instead of taking the highest exponent
Why it happens: When you add all the exponents together, you are just multiplying 12 × 18 = 216 and double-counting the shared 2 and 3.
Using (a × b × c) ÷ GCF(a, b, c) for three numbers
Why it happens: In a group of three numbers, two pairs can overlap even more than the three-way GCF accounts for.
Forgetting to include primes that only appear in one number
Why it happens: Only keeping shared primes gives you the Greatest Common Factor (GCF), not the Least Common Multiple.
Stopping a factor tree on a composite number like 4, 6, or 9
Why it happens: Prime exponent comparison only works when the bases are prime numbers (2, 3, 5, 7, 11, 13…).
Dividing by a composite number mid-way through a Cake Ladder
Why it happens: Sticking to prime divisors guarantees you never overlook a partial overlap between two of the remaining numbers.
Assuming the product a × b is always the LCM
Why it happens: 96 is a common multiple of 8 and 12, but it is four times larger than the LEAST common multiple.
Getting an answer smaller than the largest input number
Why it happens: 30 does not divide evenly into 15! A sanity check before you move on: your LCM must always be at least as large as the biggest number in your problem.
The 5-Second Test Check
Before you move to the next question on a quiz, divide your LCM answer by each starting number. If every division gives a whole number—and your answer isn't an obvious double of a smaller common multiple—you know it is right. You can see this check in action on our Main LCM Calculator.