Quick Decision Chart: Which Method Should You Use?
| Method | Best Situation | Avoid When… |
|---|---|---|
| 1. Listing Multiples | 2 small numbers under 12 (like 4 and 6, or 6 and 9) | The answer is more than 8–10 steps down the times table |
| 2. Prime Factorization | 3 or more numbers, or medium numbers from 12 to 500 | Numbers are huge and hard to factor without a calculator |
| 3. GCF Formula | Exactly 2 numbers (especially large ones using Euclidean steps) | You have 3+ numbers and forget to apply it pairwise |
| 4. Cake / Ladder | Visual learners solving 2 to 4 composite numbers on paper | None of the numbers share any common prime factors |
Method 1: Listing Multiples (12, 18, and 24)
Start with the largest number in your list (24) and count up by 24s. At each step, check whether 12 and 18 divide evenly into it:
- 24 × 1 = 24 → 12 divides 24 (24 ÷ 12 = 2), but 18 does not.
- 24 × 2 = 48 → 12 divides 48 (48 ÷ 12 = 4), but 18 does not.
- 24 × 3 = 72 → 12 divides 72 (6) AND 18 divides 72 (4). Match found!
Teacher tip: Stepping by the largest number first (24, 48, 72) took only 3 checks, whereas stepping by 12 would have taken 6 checks.
Method 2: Prime Factorization with Exponents
Break each number down to prime factors using a factor tree, then write repeated primes with exponents:
Scan each prime and pick the largest exponent that appears in any single line:
- Highest power of 2 is 2³ = 8 (from 24).
- Highest power of 3 is 3² = 9 (from 18).
LCM(12, 18, 24) = 2³ × 3² = 8 × 9 = 72.
Method 3: The Pairwise GCF Formula
Using LCM(a, b) = (a × b) ÷ GCF(a, b), combine the first two numbers, and then combine that answer with the third number:
Method 4: The Cake / Ladder Division Grid
Write 12, 18, and 24 in a row and divide out shared prime factors one layer at a time:
Multiply the outside L-shape: 2 × 3 × 2 × 1 × 3 × 2 = 72. You can view this exact ladder interactively on our Main LCM Calculator.