How to Find the LCM of Three or More Numbers (2026 Tutorial)

While finding the Least Common Multiple (LCM) of two numbers is straightforward, finding it for three, four, or more numbers can quickly become confusing. However, the principles remain identical. By extending prime factorization or using the division ladder, you can solve larger sets of numbers easily.

In this step-by-step tutorial, we will show you how to find the LCM of multiple numbers with clear, worked examples.

Method 1: Prime Factorization (Best for larger numbers)

To find the LCM of 12, 15, and 18 using prime factorization:

1. Write Prime Factorizations:
   • 12 = 2^2 * 3^1
   • 15 = 3^1 * 5^1
   • 18 = 2^1 * 3^2
2. List All Prime Factors: The prime factors involved are 2, 3, and 5.
3. Take Highest Exponents:
   • Highest power of 2 is 2^2 (from 12)
   • Highest power of 3 is 3^2 (from 18)
   • Highest power of 5 is 5^1 (from 15)
4. Multiply Together: LCM = 2^2 * 3^2 * 5^1 = 4 * 9 * 5 = 180.

For instant solutions and animated factor trees, check out our Prime Factorization Tool.

Method 2: The Division Ladder (Best for multiple numbers)

The division ladder (or cake method) is incredibly efficient for three or more numbers. You write the numbers in a row and divide them by the smallest prime that divides at least two of the numbers, bringing down any numbers that aren't divisible. You repeat until no two numbers share a common factor, then multiply the divisors along the side and bottom.

Try entering your numbers into our LCM Calculator to see the division ladder rendered step-by-step automatically!

Practical Worked Example (LCM of 8, 12, 15, 20)

By entering 8, 12, 15, and 20 into the tool, the system performs the prime factorization or division method to output the exact LCM of 120, rendering each step clearly so you can trace the division path.

Worked example: LCM of 8, 12, 30

Factor each number: 8 = 2³, 12 = 2² × 3, 30 = 2 × 3 × 5. Take the highest power of every prime that appears anywhere — 2³, 3¹ and 5¹, and multiply: 8 × 3 × 5 = 120. Check: 120 ÷ 8 = 15, 120 ÷ 12 = 10, 120 ÷ 30 = 4, all whole, so 120 is indeed the least common multiple of all three. The LCM Calculator shows this prime-power table for any set of numbers.

A common shortcut and its limit

For two numbers, LCM = a × b ÷ GCF is the fastest route. But this shortcut does not work directly for three or more numbers — you cannot simply divide the product by the overall GCF. Instead, fold pairwise: LCM(8, 12) = 24, then LCM(24, 30) = 120. Each step uses the two-number formula on the running result. Prime factorization avoids the folding entirely by handling every number at once, which is why it is the preferred method as the count of numbers grows.

Worked example: LCM of 6, 8 and 15

The LCM of three or more numbers is easiest by prime factorization. Write each in primes: 6 = 2 × 3, 8 = 2³, 15 = 3 × 5. Take the highest power of every prime that appears anywhere: 2³ (from 8), 3 (from 6 or 15) and 5 (from 15). Multiply: LCM = 8 × 3 × 5 = 120. You can confirm by the pairwise method: LCM(6, 8) = 24, then LCM(24, 15) = 120 — the same answer the LCM Calculator gives for the whole list at once.

Pairwise folding vs. all-at-once

There are two reliable strategies for long lists. Pairwise folding takes the LCM of the first two numbers, then combines that result with the third, and so on — simple to do by hand and the method most calculators use internally. All-at-once prime factorization lists every number’s primes and takes the highest power of each; it is faster to see for four or five numbers and avoids carrying large intermediate values. Both always reach the same LCM, because the highest power of each prime is the same whether you combine numbers two at a time or all together.