Unlocking the Mystery of Least Common Multiple (LCM): Methods and Examples

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:

1. Prime Factorization:
   • Find the prime factorization of each number.
   • For example, let’s find the prime factorization of 12 and 18:
     • 12=2²×3
     • 18=2×3²
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: 2²,3
     • Uncommon factors (unique to each number): 2,3²
3. Multiply the Factors:
   • Multiply all the common and uncommon prime factors:

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

1. Simplify:
   • Simplify the result if possible:

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

Example: Find the LCM of 12 and 18.

1. Prime Factorization:
   • 12=2²×3
   • 18=2×3²
2. Identify Common and Uncommon Factors:
   • Common factors: 2²,3
   • Uncommon factors: 2,3²
3. Multiply the Factors:

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

1. 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.