Discover efficient methods for calculating the Least Common Multiple (LCM) with comprehensive examples. Learn step-by-step procedures to find the smallest common multiple of two or more numbers. Master the prime factorization technique and boost your mathematical skills effortlessly.

## Least Common Multiple (LCM): Methods and Examples

#### What is LCM in math

#### LCM **Definition with Example:**

The Least Common Multiple (LCM) of two or more integers is the smallest positive integer that is divisible by each of the given integers without leaving a remainder.

#### LCM **Full Form:**

LCM stands for “Least Common Multiple.”

**Method to Find LCM:**

There are several methods to find the LCM of two or more numbers, but one common method is the prime factorization method. Here are the steps:

**Prime Factorization:**- Find the prime factorization of each number.
- For example, let’s find the prime factorization of 12 and 18:
- 12=2
^{2}×3 - 18=2×3
^{2}

- 12=2

**Identify Common and Uncommon Factors:**- Identify the common and uncommon prime factors. Include each prime factor the maximum number of times it occurs in any of the given numbers.
- Common factors: 2
^{2},3 - Uncommon factors (unique to each number): 2,3
^{2}

- Common factors: 2

- Identify the common and uncommon prime factors. Include each prime factor the maximum number of times it occurs in any of the given numbers.
**Multiply the Factors:**- Multiply all the common and uncommon prime factors:

LCM = 2^2 \times 3 \times 2 \times 3^2

**Simplify:**- Simplify the result if possible:

LCM = 2^3 \times 3^2 = 72

**Example:** Find the LCM of 12 and 18.

**Prime Factorization:**- 12=2
^{2}×3 - 18=2×3
^{2}

- 12=2
**Identify Common and Uncommon Factors:**- Common factors: 2
^{2},3 - Uncommon factors: 2,3
^{2}

- Common factors: 2
**Multiply the Factors:**

LCM = 2^2 \times 3 \times 2 \times 3^2

**Simplify:**

LCM = 2^3 \times 3^2 = 72

Therefore, the Least Common Multiple of 12 and 18 is 72. This means that 72 is the smallest number that is evenly divisible by both 12 and 18.