Least Common Multiple

Find the Least Common Multiple (LCM) of two numbers

"Least Common Multiple" Calculator

Least Common Multiple of

and

How to Find the Least Common Multiple (LCM) of Two Numbers

What is the Least Common Multiple?

The Least Common Multiple (LCM) of two or more numbers is the smallest positive integer that is divisible by each of the given numbers without remainder. LCM is widely used in arithmetic, algebra, and when working with fractions.

Methods for Calculating LCM

There are several ways to find the least common multiple:

  • Listing multiples method — create lists of multiples for each number and find the smallest common one
  • Prime factorization — find all prime factors and take the highest power of each
  • GCD formula: LCM(a,b) = (a × b) / GCD(a,b)
  • Euclidean algorithm — efficient method for large numbers

LCM Calculation Example

Let's find the LCM of 12 and 18:

Method 1 - Listing multiples:
Multiples of 12: 12, 24, 36, 48, 60, 72...
Multiples of 18: 18, 36, 54, 72, 90...
LCM(12, 18) = 36

Method 2 - Using GCD:
GCD(12, 18) = 6
LCM(12, 18) = (12 × 18) / 6 = 216 / 6 = 36

Practical Applications of LCM

  • Adding and subtracting fractions — LCM of denominators provides common denominator
  • Solving systems of equations — finding common coefficients
  • Scheduling and planning — determining event periodicity
  • Number theory — studying properties of integers
  • Cryptography — encryption algorithms

Properties of LCM

  • LCM(a, b) ≥ max(a, b)
  • LCM(a, b) × GCD(a, b) = a × b
  • LCM(a, b) = LCM(b, a) — commutative property
  • LCM(a, LCM(b, c)) = LCM(LCM(a, b), c) — associative property
  • If GCD(a, b) = 1, then LCM(a, b) = a × b

Online LCM Calculator

Our least common multiple calculator allows you to quickly compute the LCM of any two positive numbers. Simply enter the numbers and get instant results with detailed explanation of the calculation process.

See Also

About "Least Common Multiple" Calculator

This calculator will help you find the Least Common Multiple (LCM) of two numbers. For example, it can help you find out what's the Least Common Multiple (LCM) of 6 and 8? (The answer is: 24). Select the first number (e.g. '6') and the second number (e.g. '8'). After that hit the 'Calculate' button.
Least Common Multiple (LCM) also known as the Lowest Common Multiple or Smallest Common Multiple of 2 numbers - it is the smallest positive integer that is divisible by both numbers

FAQ

What is the least common multiple of two numbers?

It is the smallest positive integer that both numbers divide into without a remainder. Multiples of 6 are 6, 12, 18, 24…, multiples of 8 are 8, 16, 24…, and 24 is the first value on both lists, so the LCM of 6 and 8 is 24. Every pair has one, because the product of the two numbers is already a common multiple.

How do you calculate the LCM without listing multiples?

Two standard routes. By prime factorization, take each prime to the highest power it reaches in either number: 12 = 2² × 3 and 16 = 2⁴, so the LCM is 2⁴ × 3 = 48. Or go through the greatest common divisor, since LCM(a, b) = a × b ÷ GCD(a, b) — for 12 and 16 that is 12 × 16 ÷ 4 = 48.

Why is the LCM used as the common denominator of fractions?

Adding fractions needs a single denominator that both original denominators divide into, and the least common multiple is the smallest one available, so the numbers stay manageable. For 1/6 + 1/8 the LCM of 6 and 8 is 24: 1/6 becomes 4/24, 1/8 becomes 3/24, and the sum is 7/24.