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Computers and Technology

How is LCM calculated?

How is LCM calculated?

The Least Common Multiple (LCM) is likewise called the Lowest Common Multiple (LCM) and Least Common Divisor (LCD). For integers a and b, denoted LCM(a,b), the LCM is the smallest high-quality integer this is calmly divisible with the aid of using each a and b. For example, LCM(2,3) = 6 and LCM(6,10) = 30 How is LCM calculated.

The LCM of or greater numbers is the smallest variety this is calmly divisible with the aid of using all numbers withinside the set We have developed an lcm-calculator to help students and teachers to quickly find LCM and compare different methods.

https://www.lcm-calculator.com/

Least Common Multiple Calculator

Find the LCM of a fixed number with this calculator which additionally indicates the stairs and the way to do the paintings.

Input the numbers you need to locate the LCM for. You can use commas or areas to split your numbers. But do now no longer use commas inside your numbers. For example, enter 2500, 1000 and now no longer 2,500, 1,000.

How to Find the Least Common Multiple LCM

This LCM calculator with steps reveals the LCM and indicates the paintings the usage of five distinct methods:

  • Listing Multiples
  • Prime Factorization
  • Cake/Ladder Method
  • Division Method
  • Using the Greatest Common Factor GCF

How to Find LCM with the aid of using Listing Multiples

  • List the multiples of every variety till at the least one of the multiples seems on all lists
  • Find the smallest variety this is on all the lists
  • This variety is the LCM

Example: LCM(6,7,21)

  • Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60
  • Multiples of 7: 7, 14, 21, 28, 35, 42, 56, 63
  • Multiples of 21: 21, 42, 63
  • Find the smallest variety this is on all the lists. We have it in ambitious above.
  • So LCM(6, 7, 21) is 42

How to locate LCM with the aid of using Prime Factorization

  • Find all of the top elements of every given variety.
  • List all of the top numbers discovered, as oftentimes as they arise most usually for any person given variety.
  • Multiply the listing of top elements collectively to locate the LCM.

The LCM(a,b) is calculated with the aid of using locating the top factorization of each a and b. Use the identical method for the LCM of greater than 2 numbers.

For example, for LCM(12,30) we locate:

  • Prime factorization of 12 = 2 × 2 × 3
  • Prime factorization of 30 = 2 × 3 × five
  • Using all top numbers discovered as frequently as ever happens most usually we take 2 × 2 × 3 × five = 60
  • Therefore LCM(12,30) = 60.

For example, for LCM(24,300) we locate:

  • Prime factorization of 24 = 2 × 2 × 2 × 3
  • Prime factorization of 300 = 2 × 2 × 3 × five × five
  • Using all top numbers discovered as frequently as ever happens most usually we take 2 × 2 × 2 × 3 × five × five = 600
  • Therefore LCM(24,300) = 600.

How to locate LCM with the aid of using Prime Factorization the usage of Exponents

  • Find all of the top elements of every given variety and write them in exponent form.
  • List all of the top numbers discovered, the usage of the best exponent discovered for every.
  • Multiply the listing of top elements with exponents collectively to locate the LCM.

Example: LCM(12,18,30)

  • Prime elements of 12 = 2 × 2 × 3 = 22 × 31
  • Prime elements of 18 = 2 × 3 × 3 = 21 × 32
  • Prime elements of 30 = 2 × 3 × five = 21 × 31 × five1
  • List all of the top numbers discovered, as oftentimes as they arise most usually for any person given variety and multiply them collectively to locate the LCM
    • 2 × 2 × 3 × 3 × five = 180
  • Using exponents instead, multiply collectively every of the top numbers with the best power
    • 22 × 32 × five1 = 180
  • So LCM(12,18,30) = 180

Example: LCM(24,300)

  • Prime elements of 24 = 2 × 2 × 2 × 3 = 23 × 31
  • Prime elements of 300 = 2 × 2 × 3 × five × five = 22 × 31 × five2
  • List all of the top numbers discovered, as oftentimes as they arise most usually for any person given variety and multiply them collectively to locate the LCM
    • 2 × 2 × 2 × 3 × five × five = 600
  • Using exponents instead, multiply collectively every one of the top numbers with the best power
    • 23 × 31 × five2 = 600
  • So LCM(24,300) = 600

How to Find LCM Using the Cake Method (Ladder Method)

The cake technique makes use of the department to locate the LCM of a fixed number. People use the cake or ladder technique because the quickest and simplest manner to locate the LCM as it is a straightforward department.

The cake technique is similar to the ladder technique, the field technique, the component field technique, and the grid technique of shortcuts to locate the LCM. The packing containers and grids would possibly appear a touch distinct, however, all of them use department with the aid of using primes to locate LCM.

Find the LCM(10, 12, 15, 75)

  • Write down your numbers in a cake layer (row)

How to Find LCM with the aid of using GCF

The system to locate the LCM the use of the Greatest Common Factor GCF of a hard and fast of numbers is:

LCM(a,b) = (a×b)/GCF(a,b)

Example: Find LCM(6,10)

  • Find the GCF(6,10) = 2
  • Use the LCM with the aid of using GCF system to calculate (6×10)/2 = 60/2 = 30
  • So LCM(6,10) = 30

An element is a variety of that consequences while you may calmly divide one range with the aid of using another. In this sense, an element is likewise referred to as a divisor.

The best, not unusualplace element of or extra numbers is the biggest range shared with the aid of using all of the factors.

The best, not unusualplace element GCF is equal as:

  • HCF – Highest Common Factor
  • GCD – Greatest Common Divisor
  • HCD – Highest Common Divisor
  • GCM – Greatest Common Measure
  • HCM – Highest Common Measure

How to Find LCM of Decimal Numbers

  • Find the range with the maximum decimal locations
  • Count the range of decimal locations in that range. Let’s name that range D.
  • For every one of your numbers pass the decimal D locations to the right. All numbers become integers.
  • Find the LCM of the set of integers
  • For your LCM, pass the decimal D locations to the left. This is the LCM to your unique set of decimal numbers How is LCM calculated.

 

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