Lowest Common Multiple Calculator

Calculate the LCM of two or more numbers with detailed step-by-step solutions. Our calculator shows multiple methods to help you understand the process.

Enter Numbers (separated by commas):

What is the Lowest Common Multiple?

The Lowest Common Multiple (LCM) is the smallest positive number that is divisible by two or more given numbers. It represents the first common multiple shared by all the numbers in question.

Example: The LCM of 6 and 8 is 24, because 24 is the smallest number that both 6 and 8 divide into evenly (6 × 4 = 24 and 8 × 3 = 24).

Methods to Find LCM

1. Listing Multiples Method

List the multiples of each number until you find the first common multiple.

Example: LCM of 4 and 6
Multiples of 4: 4, 8, 12, 16, 20, 24…
Multiples of 6: 6, 12, 18, 24…
LCM = 12

2. Prime Factorisation Method

Break each number into its prime factors, then multiply the highest powers of all prime factors.

Example: LCM of 12 and 18
12 = 2² × 3
18 = 2 × 3²
LCM = 2² × 3² = 4 × 9 = 36

3. Division Method

Divide the numbers by prime factors systematically until all results are 1, then multiply all divisors.

Applications of LCM

Fractions: Finding common denominators when adding or subtracting fractions
Time Problems: Calculating when recurring events will coincide
Scheduling: Determining optimal timing for repeating activities
Mathematics: Solving equations and working with algebraic expressions

LCM vs HCF

Whilst LCM finds the smallest common multiple, the Highest Common Factor (HCF) finds the largest number that divides into all given numbers. Both concepts are fundamental in number theory and have practical applications in mathematics.

Key Relationship: For any two numbers a and b:
LCM(a,b) × HCF(a,b) = a × b

Frequently Asked Questions

What’s the difference between LCM and LCF?

LCM (Lowest Common Multiple) finds the smallest common multiple, whilst LCF would refer to Lowest Common Factor, which isn’t a standard mathematical term. The correct comparison is between LCM and HCF (Highest Common Factor).

Can the LCM be smaller than the largest input number?

No, the LCM is always greater than or equal to the largest number in the set. If one number is a multiple of all others, then that number is the LCM.

How do I find the LCM of three or more numbers?

Calculate the LCM of the first two numbers, then find the LCM of that result with the third number, and continue this process for additional numbers.

What if I need the LCM of decimal numbers?

Convert decimals to whole numbers by multiplying by appropriate powers of 10, find the LCM, then divide by the same power of 10.