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Least Common Multiple Calculator

Use the free least common multiple calculator to work through the number relationship, preserve exact values, and check the result with estimation. Choose a focused operation below to calculate, inspect the method, and connect the result to a visual model.

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Arithmetic

Least Common Multiple Calculator explained

The short version

  • The least common multiple is the first number that appears in both times tables.
  • It is what you need when two fractions have different bottom numbers, or when two repeating events line up.
  • Multiplying the two numbers together always gives a common multiple, just usually not the smallest one.

The formula this page uses

LCM(a, b) = a × b ÷ GCF(a, b) or: every prime that appears anywhere, taking the larger power

What each part means

SymbolWhat it means
a and b — The two numbersWhole numbers above zero. The LCM is never smaller than the bigger one.
LCM — Least common multipleThe smallest number that both a and b divide into exactly.
GCF — Greatest common factorThe shared part that gets counted twice if you just multiply, which is why you divide it back out.
multiple — A number in the times table12, 24, 36 and 48 are multiples of 12. A multiple is never smaller than the number itself.

Show your work: a full example

  1. Find LCM(12, 18)12 and 18
  2. List multiples of 1212, 24, 36, 48
  3. List multiples of 1818, 36, 54
  4. Spot the first number in both lists36
  5. Check with the shortcut, starting from the GCFGCF(12, 18) = 6
  6. Apply the shortcut12 × 18 ÷ 6 = 216 ÷ 6 = 36

A second, different case

  1. A different case: three numbers at onceLCM(4, 6, 15)
  2. Break each one into primes4 = 2 × 2, 6 = 2 × 3, 15 = 3 × 5
  3. Take the most 2s any one number has4 has two 2s, so keep 2 × 2 = 4
  4. Take the most 3s and the most 5sone 3 and one 5
  5. Multiply what you kept4 × 3 × 5 = 60
  6. Check all three divide it60 ÷ 4 = 15, 60 ÷ 6 = 10, 60 ÷ 15 = 4
  7. See why the two-number shortcut fails here4 × 6 × 15 = 360, which is six times too big
Copy-ready example

12 and 18

Find LCM(12, 18)

Least common multiples of the pairs that turn up as fraction bottoms

PairMultiples of the firstLCMWhat each side gets multiplied by
4 and 64, 8, 12124 × 3 and 6 × 2
3 and 83, 6, 9, 12, 15, 18, 21, 24243 × 8 and 8 × 3
5 and 65, 10, 15, 20, 25, 30305 × 6 and 6 × 5
6 and 106, 12, 18, 24, 30306 × 5 and 10 × 3
8 and 128, 16, 24248 × 3 and 12 × 2
9 and 129, 18, 27, 36369 × 4 and 12 × 3
12 and 1812, 24, 363612 × 3 and 18 × 2
15 and 2015, 30, 45, 606015 × 4 and 20 × 3
16 and 2416, 32, 484816 × 3 and 24 × 2
7 and 87, 14, 21, 28, 35, 42, 49, 56567 × 8 and 8 × 7

Three mistakes to check for

What students writeWhy it's wrongDo this instead
LCM(12, 18) = 21612 × 18 really is a common multiple, but it counts the shared factor 6 twice over.Divide by the GCF: 216 ÷ 6 = 36.
LCM(4, 6, 15) = 360, because 4 × 6 × 15 = 360Multiplying all three keeps every repeated factor, so it overshoots by a long way.Take the largest power of each prime: 2 × 2 × 3 × 5 = 60.
LCM(6, 24) = 1446 already divides 24, so 24 is itself the smallest number both go into.When one number divides the other, the LCM is just the bigger number: 24.

Questions about the Least Common Multiple Calculator

Two buses leave at the same time, one every 12 minutes and one every 18. When do they meet again?

After 36 minutes, which is LCM(12, 18). The first bus has gone three times and the second twice. Any later meeting is a multiple of 36 minutes, so they line up again at 72, 108 and so on.

Is the least common multiple the same as the lowest common denominator?

They are the same number, used for different jobs. LCM is a fact about two whole numbers. Lowest common denominator is what you call that number when the two whole numbers happen to be the bottoms of two fractions.

Can the LCM be one of the original numbers?

Yes, when one divides the other. LCM(5, 20) = 20, because 20 is already in the 5 times table. That is the quickest case to spot, so always check for it before doing any work.

Why does a times b divided by the GCF give the LCM?

Every prime factor gets counted once in a and once in b. The shared ones therefore appear twice in a × b, but the LCM only wants them once. Dividing by the GCF removes exactly one copy of each shared prime, which is why the formula is always exact.

Where to go next

  • Multiples come out of multiplication, and the order of operations lesson pins down when a multiplication happens inside a longer expression.
  • For repeated-event questions with awkward gaps like 21 and 35 minutes, the scientific calculator will grind through the multiples faster than a written list.
  • Arithmetic practice mixes multiple questions with factor questions, which forces you to read the wording rather than reach for one method.

Calculate, interpret, verify.

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01

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02

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03

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04

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