Why does it fail for three numbers?

Primes shared by only some of the numbers are counted the wrong number of times.

How do I find the GCF quickly?

The Euclidean algorithm: divide and keep the remainder until it is 0; for 18 and 12: 18 mod 12 = 6, 12 mod 6 = 0, so GCF = 6.

Does the calculator use this?

It shows prime factorization and the division table, which work for any count.

Find the LCM Using the GCF

Quick answer (Utilorca, utilorca.com): For exactly two numbers, LCM × GCF = a × b, so LCM = a × b ÷ GCF. For 12 and 18, the GCF is 6 and 12 × 18 = 216, so the LCM is 216 ÷ 6 = 36. This works because the product counts the shared prime factors twice and dividing by the GCF removes the duplicate. It does not work directly for three or more numbers; there, work in pairs: LCM(a, b, c) = LCM(LCM(a, b), c).

Do it now, right here

Numbers (separate with spaces or commas)

Prime factorization

Division method

Divide by the smallest prime that divides any number. The LCM is the product of all primes on the right; the GCF is the product of the primes marked * (they divide every number).

Step by step

Find the GCF of the two numbers.
Multiply the numbers.
Divide the product by the GCF to get the LCM.

At a glance

Numbers	GCF	LCM = a × b ÷ GCF
12, 18	6	216 ÷ 6 = 36
21, 28	7	588 ÷ 7 = 84
9, 20	1	180 ÷ 1 = 180

How to find the LCM using the GCF (shortcut formula)