How to find the least common multiple of 4 and 5 and why the answer is 20

LCM and the Tiny Meeting of Two Numbers

Ever notice how two friends sometimes end up in the same place at the same time, even if they start apart? In math, there’s a similar idea called the least common multiple, or LCM. It’s the smallest number that is a multiple of both numbers involved. Pretty handy when you’re juggling fractions, schedules, or just trying to see how numbers fit together.

Let’s start with a simple, friendly example: the numbers 4 and 5. You’ve probably seen them as a pair in stories or in puzzles, but here they’re a math duo that really wants to find a shared ground.

The chase: multiples in plain sight

A good way to see the LCM is to list a few multiples of each number and look for the earliest one they share.

• Multiples of 4: 4, 8, 12, 16, 20, 24, …

• Multiples of 5: 5, 10, 15, 20, 25, …

Now, scan the two lists. What’s the first common number you spot? That’s the LCM. For 4 and 5, the first common multiple is 20. So the LCM of 4 and 5 is 20.

Why not 10 or 15? Because 10 isn’t divisible by 4, and 15 isn’t divisible by 4 either. A common multiple has to be a multiple of both numbers. When you check carefully, 20 is the smallest one that works for both.

Two quick ways to see it

There are a couple of neat shortcuts you can use without writing out long lists.

• The product-and-divide trick: If two numbers share no common factors other than 1, their LCM is just their product. For 4 and 5, gcd(4,5) = 1, so LCM(4,5) = 4 × 5 = 20.

• Prime factorization route: Write each number as prime factors, take the highest power of each prime that appears, and multiply. 4 = 2^2, 5 = 5^1. Take 2^2 and 5^1, multiply: 4 × 5 = 20.

Both routes land on the same answer, and that consistency is the beauty of these ideas. It’s like solving a small puzzle where the pieces just click.

A quick detour into why that works

If you’re curious about the “why,” here’s a simple way to think about it. Every multiple of 4 must have the factor 4 inside, every multiple of 5 must have a factor 5 inside. The smallest number that has both 4 and 5 as factors is the one that includes all the necessary prime pieces at their highest needed powers. Since 4 is 2^2 and 5 is 5^1, you need 2^2 and 5^1. Multiply them, you get 20. It’s math’s version of packing the essentials and nothing more.

LCM in everyday life: where does it show up?

You don’t need to raid a chalkboard to feel the power of the LCM. Here are a few real-world moments where it quietly helps:

• Fractions that need a common denominator. If you want to add 1/4 and 1/5, you’ll find a common ground by using the LCM of 4 and 5 as the new denominator. In this case, 20 fits the bill.

• Scheduling and timers. If you have two routines that repeat every 4 days and every 5 days, the LCM tells you when they line up again.

• Sharing chores or resources. If two tasks repeat on different cycles, the LCM helps you coordinate so both land on the same day.

A small caveat and a gentle nudge

Sometimes it’s tempting to rush to a number that looks big and claim it as the “answer.” But the LCM isn’t about being large; it’s about being the smallest number that satisfies being a multiple of both numbers. A quick check helps: is the candidate divisible by both originals? If yes, you’ve got your LCM; if not, keep looking, even if it feels like a tiny detour.

Common landmines to watch for

• Assuming the LCM is always the product of the numbers. That only happens when the numbers share no common factors besides 1. If they do share factors, you’ll often get a smaller number than the simple product.

• Forgetting that 0 has special rules. Multiples of 0 aren’t meaningful in the same way here, so steer clear in basic LCM thinking.

• Treating LCM like a random big number. It’s not random at all—it's tightly tied to the prime structure of the numbers involved.

A tiny practice moment

Let’s apply what we’ve talked about with a fresh set of numbers. What’s the LCM of 4 and 6?

• Multiples of 4: 4, 8, 12, 16, …

• Multiples of 6: 6, 12, 18, 24, …

The first common one is 12. So LCM(4,6) = 12. Quick check via prime factors: 4 = 2^2, 6 = 2 × 3. Take the highest powers: 2^2 and 3^1, multiply to get 12. Same result, same logic, just a different route.

Now try 8 and 3. Multiples: 8, 16, 24, 32, … and 3, 6, 9, 12, 15, 18, 21, 24, … The first shared is 24. LCM(8,3) = 24. You can see how the method scales up or down depending on what you’re working with.

Why this matters for math intuition

Learning LCM isn’t just about passing a set of questions or labeling a number right. It’s about noticing patterns, about seeing how different pieces fit together. That kind of mindset helps when you encounter fractions, algebraic expressions, or even geometry problems that lean on common frequency or overlap. It makes math feel less like a wall and more like a puzzle that you’re solving, piece by piece.

A few reflective notes

• The LCM teaches patience in a small classroom of numbers. You don’t have to sprint; you just keep checking multiples until you find the first ally.

• It’s a friendly reminder that math has rules, but those rules are consistent and kind of elegant when you follow them step by step.

• If you ever feel stuck, switch to a different path—the prime-factor route often shines a light when the simple listing feels heavy.

To wrap it up

So, the smallest common multiple of 4 and 5 isn’t a mystery. It’s 20—the friend they share as a multiple, and it’s the clean product of their distinct prime pieces. Whether you’re adding fractions, aligning schedules, or just spotting neat number relationships, LCMs are the sort of tiny tools that quietly boost your math fluency.

If you’re curious to test this idea with other pairs, a few quick challenges are waiting. Try 9 and 12, or 7 and 11, and see how the little meeting point shows up again. The more you play with these ideas, the more you’ll notice how numbers have their own conversations, and how those conversations settle into patterns you can predict and explain.

Helpful reminder: LCM is not about being flashy; it’s about being precise. It’s the smallest number that makes sense for both players in the pair, and that clarity is what makes math feel confident rather than mysterious. And that confidence—that quiet certainty—is a small, steady win in any math moment you might encounter.