Least Common Multiple

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : May 22, 2023

Are you searching for the stuff related to the Least Common Multiple Concept? Simply, you have come to the right place. Here, you all will get to know, learn, & understand the concept called Least Common Multiple (LCM). In mathematics, LCM is the most commonly used calculation for finding solutions to various math problems. So, getting a great grip on the LCM Concept is a must.

Ex: Least Common Multiple of 12, 48, 64 (or) Least Common Multiple of 16, 56, 22 (or) Least Common Multiple of 8, 72, 48

Least Common Multiple of:

Here are some samples of Least Common Multiple of Numbers calculations.

Related Calculators:

Hence, we have compiled all the things about Least common multiple on this page right from definitions to various methods to find it. In addition to this, you can also find out free online & handy tools to determine the Least common multiple with ease and quick. Refer to the below sections & learn all about LCM of two numbers, LCM of three or more numbers, etc.

List of Least Common Multiple Calculators

Excited to use all these handy & instant online Least common multiples for attaining quick results? then, make use of the accessible links available over here and pick the suitable LCM calculator to solve the least common multiple of given numbers.

  • LCM Calculator
  • LCM of two Numbers Calculator
  • LCM of 3 Numbers Calculator
  • LCM of 4 Numbers Calculator
  • LCM of 5 Numbers Calculator
  • LCM of Decimals Calculator
  • LCM of Fractions Calculator
  • LCD Calculator
  • How to find LCM
  • LCM Questions

To understand the concept clearly & easily, we have also compiled the detailed procedures and solved examples for each of the LCM related concepts. You can even learn the definitions for multiple, common multiple, Least Common Multiple, other names, why it is useful, and also various techniques on how to find the LCM of numbers.

All Basics About Least Common Multiple (LCM)

Okay, let's not waste the time just go ahead and learn all the information about Least Common Multiple like what is multiple, common multiple, least common multiple, how to find LCM with various methods, etc. from the further sections. Now, we will start with fundamentals to understand easily about the LCM and how to solve it if we have two or more numbers as inputs?

What is meant by Multiple?

In maths, Multiple means the product result of one number multiplied by another number. Also, the definition of Multiple is a number that may be divided by another a certain number of times without a remainder.

For instance, multiples of 4 are 4,8,12,16,20,24,28,32,36,40,44,... (just like the 4th multiplication table)

What is Common Multiple?

A common multiple is a whole number that is a shared multiple of each set of numbers. The multiples that are common to two or more numbers are called the common multiples of those numbers.

Example: Find the common multiples of 3 and 4, already we have listed the multiples of 4 above, now list out the multiples of 3 and then find their common multiples.

Multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, ...

Multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, ....

The common multiples of 3 and 4 are 12, 24, 36.

Definition of Least Common Multiple

The Least Common Multiple is the smallest positive integer that is divisible by the given numbers. The representation of the Least Common Multiple is LCM and it is denoted by lcm(a, b).

Example:

Let's consider the above example and find the least common multiple of 3 and 4?

At first, list out the common multiples of 3, 4 and then find the smallest common multiple as LCM of 3, 4.

The common multiples of 3 and 4 are 12, 24, 36.

The Least Common Multiple of 3 and 4 is 12 (smallest number).

Least Common Multiple Other Names

LCM is the short form of Least Common Multiple and also it is named as the lowest common multiple or smallest common multiple or Least Common Denominator(LCD) or Lowest Common Factor(LCF).

Why is LCM or LCD Useful?

Every student is somewhat aware of the least common multiple problems and the benefit. But the concept of L.C.M. is necessary to determine problems related to racetracks, traffic lights, etc. Instead of these, you may also come to know that LCM is useful to determine the smallest number that divides all given numbers evenly. The least common multiple tools are used to solve the LCM of given numbers much easier and faster.

Various Methods to Solve the Least Common Multiple (LCM)

Want to know what are the different ways to solve the LCM of given numbers? Then, check out the list of various methods that are used to find the least common multiple of two numbers, LCM of three numbers, LCM of 4 or 5 numbers here. Use these prominent techniques by accessing the below links and get the exact results for LCM of numbers.

  • LCM using Listing Multiples Method
  • Least Common Multiple by Prime Factorization Method
  • LCM using Cake/Ladder Method
  • LCM by Division Method
  • LCM Using the Greatest Common Factor Formula

A step by step procedure on how to find the least common multiple using these various methods is provided in the above-given links. Access the links & make use of the detailed explanation and illustrated show work to learn and understand the concept of Least Common Multiple (LCM).

If you are willing to grasp the Greatest Common Factor (GCF) or LCD concepts then visit lcmgcf.com a reliable source that offers free & handy tools to help students finish their work easily & understand the concept in a better way.