Lowest Common Multiple Of 18 And 24

What's the smallest number that both 18 and 24 divide into cleanly?

Most people hit up their phone calculator when they run into a problem like this, but there's actually a method that works for any pair of numbers — and it's not as complicated as you might think. The answer for 18 and 24 is 72, but here's how you actually get there without guessing.

What Is the Lowest Common Multiple?

The lowest common multiple (LCM) of two numbers is the smallest positive integer that both numbers divide into evenly. So for 18 and 24, we're looking for the smallest number that both 18 and 24 go into without leaving a remainder.

It's worth noting that the LCM isn't the same as the greatest common divisor (GCD). While GCD finds the largest number that divides both numbers, LCM finds the smallest number that both numbers divide into. They're related, but they solve different problems.

Why You Actually Need This

Most people wonder why they should care about finding LCMs. Turns out, it's more useful than you'd expect. Here's the thing — adding fractions with different denominators? Now, you need the least common denominator, which is just the LCM of the denominators. Planning events, organizing groups, even certain coding problems—all of them pop up in real work.

How to Find the LCM of 18 and 24

There are a few ways to tackle this, and each has its own strengths. Let me walk you through the most reliable methods.

Method 1: Listing Multiples

This is the most straightforward approach. You list out multiples of each number until you find a match.

Multiples of 18: 18, 36, 54, 72, 90, 108... Multiples of 24: 24, 48, 72, 96, 120...

There it is—72 appears in both lists, and it's the first match. That's your LCM.

This method works fine for smaller numbers, but try it with 48 and 54 and you'll be listing numbers for a while. It's reliable but can get tedious.

Method 2: Prime Factorization

This is where things get interesting. You break each number down into its prime components and then multiply the highest power of each prime together.

For 18: 18 = 2 × 3² For 24: 24 = 2³ × 3

Now you take the highest power of each prime: 2³ and 3². Multiply them together: 8 × 9 = 72.

This method scales much better for larger numbers and gives you a clear understanding of why the LCM works the way it does.

Method 3: Using the Formula

There's actually a direct relationship between LCM and GCD that you can exploit: LCM(a, b) = (a × b) ÷ GCD(a, b).

First, find GCD(18, 24):

Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Greatest common factor: 6

Now plug it in: (18 × 24) ÷ 6 = 432 ÷ 6 = 72

This formula is incredibly handy when you're working with a calculator or programming, but it does require you to find the GCD first.

Common Mistakes People Make

Here's what most folks get wrong when calculating LCM:

They stop too early. I've seen people list a few multiples and call it done. "Oh, 18 and 24 both go into 48!" But wait—does 24 go into 48? Yes, that's 2 times. But 18 goes into 48 two times with a remainder of 12. Not a clean division.

They confuse LCM with GCD. These are completely different operations. The GCD of 18 and 24 is 6, not 72. Mixing these up gives you answers that are way off.

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They miss prime factors. When doing prime factorization, it's easy to forget that 18 = 2 × 3 × 3, not just 2 × 3. Missing that extra 3 means you'll get 24 instead of 72.

They multiply the numbers directly. Some people think LCM is just multiplying the two numbers together. 18 × 24 = 432. That's technically a common multiple, but it's not the lowest one. It's like running a marathon instead of walking to the store when you just need to grab milk.

Practical Tips That Actually Work

After working through dozens of these problems, here are the strategies that save time:

Start with prime factorization for numbers over 20. It's more systematic and less prone to human error than listing multiples. You can do it in your head or on paper, and it works every time.

Use the GCD formula when you're stuck. If listing multiples feels messy, try finding the GCD first. Euclidean algorithm makes this quick: divide the larger number by the smaller, find the remainder, repeat with the divisor and remainder until you hit zero. The last non-zero remainder is your GCD.

Check your work by dividing. Once you think you have the LCM, divide both original numbers into your answer. If both divisions are clean (no decimals or remainders), you're good. If not, keep going.

For 18 and 24 specifically: Remember that 24 is 4 × 6, and 18 is 3 × 6. Since 24 already contains the 4 and 6, you just need to add the missing 3 to get 72. This mental shortcut works surprisingly well.

Quick Verification

Let's double-check our answer. Does 72 work?

72 ÷ 18 = 4 ✓ 72 ÷ 24 = 3 ✓

Both divide evenly. Is there a smaller number? We checked the multiples and prime factors—72 is indeed the smallest.

Frequently Asked Questions

Is the LCM always bigger than both original numbers?

Not necessarily. Which means for example, LCM of 6 and 12 is 12, not something bigger. If one number is a multiple of the other, the LCM is the larger number. But for 18 and 24, neither is a multiple of the other, so the LCM (72) is larger than both.

Can I find LCM of more than two numbers?

Absolutely. You apply the same principles—either find common multiples or use prime factorization across all numbers. Take the highest power of each prime that appears, multiply them together.

What if the numbers have no common factors?

If two numbers share no common factors besides 1 (they're coprime), their LCM is simply their product. Take this case: LCM of 5 and 7 is 35 because they share no common factors.

Does LCM work with negative numbers?

Technically yes, but it's rarely needed in practice. Day to day, the LCM is defined as the smallest positive integer, so you'd take the LCM of the absolute values. In most contexts, we stick to positive integers.

Can LCM be a prime number?

Only if one of the original numbers is that prime. As an example, LCM of 7 and 14 is 14, not a prime. But LCM of 7 and 11 is 77, which isn't prime either. When both numbers are prime and different, their LCM is their product, which is never prime.

The Bigger Picture

Finding LCM isn't just an academic exercise—it's a tool that shows up when you need things to line up. Whether you're synchronizing gears in machinery, planning recurring events, or just solving fraction problems, the LCM gives you the framework to find that perfect alignment point.

For 18 and 24, the answer is 72. But the real value is understanding how you got there, so next time you face a similar problem, you've got multiple paths to choose from.