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What is full form LCM?

Published in Mathematics 3 mins read

The full form of LCM is Least Common Multiple.

The Least Common Multiple (LCM) is a fundamental concept in mathematics, particularly in number theory. It refers to the smallest positive integer that is perfectly divisible by two or more given numbers. Understanding the LCM is crucial for solving various arithmetic problems, especially those involving fractions and ratios.

Understanding the LCM

Let's break down the concept:

  • Multiple: A multiple of a number is obtained by multiplying that number by any integer. For example, multiples of 3 are 3, 6, 9, 12, and so on.
  • Common Multiple: A common multiple of two or more numbers is a number that is a multiple of each of those numbers. For example, common multiples of 2 and 3 are 6, 12, 18, etc.
  • Least Common Multiple: The smallest of these common multiples is the least common multiple (LCM). In the example above, the LCM of 2 and 3 is 6.

How to Find the LCM

There are several methods to find the LCM of two or more numbers:

  1. Listing Multiples: List the multiples of each number until you find a common multiple. The smallest common multiple is the LCM. This method is suitable for small numbers.

    • Example: Find the LCM of 4 and 6.
      • Multiples of 4: 4, 8, 12, 16, 20, 24,...
      • Multiples of 6: 6, 12, 18, 24, 30,...
      • The LCM of 4 and 6 is 12.

  2. Prime Factorization: Express each number as a product of its prime factors. Then, take the highest power of each prime factor that appears in any of the numbers and multiply them together.

    • Example: Find the LCM of 12 and 18.
      • Prime factorization of 12: 22 x 3
      • Prime factorization of 18: 2 x 32
      • LCM = 22 x 32 = 4 x 9 = 36

  3. Division Method: Divide the numbers simultaneously by a common prime factor. Continue until no common prime factor exists. The LCM is the product of all the divisors and the remaining numbers.

    • Example: Find the LCM of 15 and 20.
    15 20
    5 3 4
    • LCM = 5 x 3 x 4 = 60

Importance of LCM

  • Fractions: LCM is essential when adding or subtracting fractions with different denominators. You need to find the LCM of the denominators to obtain a common denominator.
  • Ratios and Proportions: LCM can be useful in solving problems involving ratios and proportions, especially when dealing with whole numbers.
  • Scheduling Problems: LCM can help determine when events will coincide if they occur at regular intervals.

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