How do I find the least common multiple of 18 and 24?

Their GCD is 6. Divide 18 by 6 and multiply by 24: LCM = 72.

What is the least common multiple of 18, 24 and 30?

First find LCM(18, 24) = 72, then LCM(72, 30) = 360.

Is lowest common multiple the same as least common multiple?

Yes. Both names refer to the LCM. For positive inputs it is the smallest positive integer divisible by every input.

Can the calculator handle zero, negative numbers and decimals?

Negative integers use their absolute values. A zero input returns LCM = 0 by convention. Decimal values are not supported.

When is the LCM equal to the product of two numbers?

For two positive coprime integers, the GCD is 1, so the LCM equals their product.

Find Least Common Multiple: LCM Methods, Examples and Calculator

To find the least common multiple of positive integers, choose the smallest number divisible by every input. Learn three methods, check worked examples and use the free LCM calculator for exact results.

Quick answer: how to find the least common multiple

For two positive integers a and b, LCM(a, b) = (a ÷ GCD(a, b)) × b. Find the greatest common divisor, divide one input by it, then multiply by the other. For 18 and 24, the GCD is 6, so LCM = (18 ÷ 6) × 24 = 72.

Least common multiple, lowest common multiple and LCM refer to the same quantity. A multiple is a number obtained by multiplying an integer by a whole number. For nonzero inputs, we seek the smallest positive common multiple.

Method 1: list multiples for small numbers

List positive multiples of 6: 6, 12, 18, 24, 30, …
List positive multiples of 8: 8, 16, 24, 32, …
The first shared value is 24, so LCM(6, 8) = 24.

Listing multiples makes the idea visible, but it becomes slow when the answer is large. Finding any common multiple is not enough: the result must be the smallest positive one.

Method 2: use prime factorization

Factor 18 = 2 × 3² and 24 = 2³ × 3.
Take the largest exponent of each prime appearing in either number: 2³ and 3².
Multiply those powers: 2³ × 3² = 8 × 9 = 72.

Do not add the exponents or keep only the shared primes. The LCM includes all necessary prime factors at their highest powers. Keeping shared primes at the smallest powers gives the GCD instead.

Method 3: use the greatest common divisor

For 18 and 24, use Euclid’s algorithm: 24 mod 18 = 6; 18 mod 6 = 0. Therefore GCD = 6.
Divide before multiplying: 18 ÷ 6 = 3, then 3 × 24 = 72.
Check divisibility: 72 ÷ 18 = 4 and 72 ÷ 24 = 3.

Divisibility confirms that a candidate is a common multiple. The GCD formula or prime-factor method establishes that it is the least one. Toolnoza uses exact integer arithmetic for this calculation.

Find the LCM of three or more numbers

Combine the numbers pairwise: LCM(18, 24, 30) = LCM(LCM(18, 24), 30). First find 72. Since GCD(72, 30) = 6, the next result is (72 ÷ 6) × 30 = 360.

The same approach extends to a longer list. Input order changes the intermediate steps but not the final LCM. Repeated values do not change the result.

Use the LCM calculator online

Open Toolnoza’s Least Common Multiple Calculator using the button above.
Enter 2–20 integers separated by spaces, commas, semicolons or line breaks. For this example, enter 18, 24, 30.
Read the result 360 and the pairwise GCD/LCM steps. Copy the result if needed.

Each input accepts up to 30 digits. Negative integers are converted to their absolute values. If an input is zero, the calculator returns zero by convention. Decimal values are not supported. Your inputs are processed in the browser.

Common denominators and repeating schedules

For 1/6 + 1/8, the LCM of 6 and 8 is 24. Rewrite the fractions as 4/24 and 3/24, then add them to get 7/24. The LCM supplies a common denominator; it does not add the numerators for you.

If two events start together and repeat every 6 and 8 days, they coincide after 24 days. Different starting offsets require additional reasoning: the LCM of the periods alone does not determine the next meeting.

Avoid these common mistakes

Multiplying all inputs gives a common multiple, but it is usually too large. For 6 and 8, the product is 48 while the LCM is 24. The product equals the LCM when the positive inputs are coprime.

Do not confuse LCM with GCD: GCD(18, 24) = 6, while LCM(18, 24) = 72. When one positive number divides the other, their LCM is the larger number; LCM(5, 20) = 20.