What is LCM (Least Common Multiple Calculator)?

LCM (Least Common Multiple) calculator is a tool that is used to find the smallest multiple that two or more numbers have in common. The LCM is the smallest positive integer that is divisible by each of the given numbers without leaving a remainder. These calculators can take a set of numbers as input and compute their LCM, making it easier for users to find the LCM without manually calculating it themselves. They are commonly used in various mathematical applications, such as in algebra, number theory, and problem-solving.

Brute Force Method

One method to find the LCM is the “brute force” approach, where you list out the multiples of each integer until a common multiple is found. For example:

Example: Find LCM(12, 18)

• 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180…
• 18: 18, 36, 54, 72, 90, 108, 126, 144, 162, 180…

As seen, this method can be tedious and impractical for larger numbers.

Prime Factorization Method

A more systematic approach is using prime factorization. Break down each number into its product of prime numbers and determine the LCM by multiplying the highest power of each prime. For example:

Example: Find LCM(15, 24, 36)

• 15 = 3 × 5
• 24 = 2 × 2 × 2 × 3
• 36 = 2 × 2 × 3 × 3

The LCM is then calculated as 2^3 × 3^2 × 5 = 360.

Greatest Common Divisor Method

Another method involves using the greatest common divisor (GCD) or greatest common factor (GCF). The procedure is to divide the product of the numbers by their GCD, i.e., (a × b)/GCD(a, b). For example:

Example: Find LCM(15, 24, 36)

• GCF(24, 36) = 12
• LCM(24, 36) = (24 × 36) / 12 = 72
• GCF(72, 15) = 3
• LCM(72, 15) = (72 × 15) / 3 = 360

Thus, LCM(15, 24, 36) is 360.

Find GCF of any numbers here – GCF Calculator

Each method has its merits, and the choice depends on the specific situation and preferences of the user.