What is LCM?

The LCM is the least not unusualplace a couple of or lowest not unusualplace a couple of among or greater numbers. We can discover the least not unusualplace a couple of via way of means of breaking down every quantity into its top elements. This may be carried out via way of means of hand or via way of means of the usage of the component calculator or top factorization calculator. The approach for locating the LCM, together with an instance illustrating the approach, could be visible withinside the subsequent section.

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

Calculator Use

The Least Common Multiple (LCM) is likewise known as the Lowest Common Multiple (LCM) and Least Common Divisor (LCD). For integers a and b, denoted LCM(a,b), the LCM is the smallest fantastic integer this is frivolously divisible through each a and b. For example, LCM(2,3) = 6 and LCM(6,10) = 30.

The LCM of or greater numbers is the smallest quantity this is frivolously divisible through all numbers withinside the set.

Least Common Multiple Calculator

Find the LCM of a fixed number with this calculator which additionally indicates the stairs and a 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 use of five exceptional methods:

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

How to Find LCM through Listing Multiples

• List the multiples of every quantity till at the least one of the multiples seems on all lists
• Find the smallest quantity this is on all the lists
• This quantity 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 quantity this is on all the lists. We have it in formidable above.
• So LCM(6, 7, 21) is 42

How to locate LCM through Prime Factorization

• Find all of the high elements of every given quantity.
• List all of the high numbers determined, as oftentimes as they arise most usually for anyone given quantity.
• Multiply the listing of high elements collectively to locate the LCM.

The LCM(a,b) is calculated by locating the high factorization of each a and b. Use the equal 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 high numbers determined as frequently as everyone takes place 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 high numbers determined as frequently as everyone takes place most usually we take 2 × 2 × 2 × 3 × five × five = 600
• Therefore LCM(24,300) = 600.

How to locate LCM through Prime Factorization the use of Exponents

• Find all of the high elements of every given quantity and write them in exponent form.
• List all of the high numbers determined, the use of the best exponent determined for every.
• Multiply the listing of high 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 high numbers determined, as oftentimes as they arise most usually for anyone given quantity and multiply them collectively to locate the LCM
  • 2 × 2 × 3 × 3 × five = 180
• Using exponents instead, multiply collectively each of the high 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 high numbers determined, as oftentimes as they arise most usually for anyone given quantity and multiply them collectively to locate the LCM
  • 2 × 2 × 2 × 3 × five × five = 600
• Using exponents instead, multiply collectively each of the high 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 an easy department.

The cake technique is similar to the ladder technique, the container technique, the thing container technique, and the grid technique of shortcuts to locate the LCM. The packing containers and grids may appearance a bit exceptional, however, all of them use department through primes to locate LCM.

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

• Write down your numbers in a cake layer (row)
• Divide the layer numbers through a high quantity this is frivolously divisible into or greater numbers withinside the layer and convey down the end result into the following layer.
• If any quantity withinside the layer isn't frivolously divisible simply carry down that quantity.
• Continue dividing cake layers through high numbers.
• When there aren't anyt any greater primes that frivolously divided into or greater numbers you're done.
• The LCM is manufactured from the numbers withinside the L shape, left column, and backside row. 1 is ignored.
• LCM = 2 × 3 × five × 2 × five
• LCM = 300
• Therefore, LCM(10, 12, 15, 75) = 300

How to Find the LCM Using the Division Method

Find the LCM(10, 18, 25)

• Write down your numbers in a pinnacle desk row
• Starting with the bottom high numbers, divide the row of numbers through a high quantity this is frivolously divisible into at the least one in every one of your numbers and convey down the end result into the following desk row.
• If any quantity withinside the row isn't frivolously divisible simply carry down that quantity.
• Continue dividing rows through high numbers that divide frivolously into at the least one quantity.
• When the ultimate row of outcomes is all 1's you're done.

 

The LCM is manufactured from the high numbers withinside the first column.

• LCM = 2 × 3 × 3 × five × five
• LCM = 450
• Therefore, LCM(10, 18, 25) = 450

How to Find LCM through GCF

The formulation to locate the LCM the use of the Greatest Common Factor GCF of a fixed 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 through GCF formulation to calculate (6×10)/2 = 60/2 = 30
• So LCM(6,10) = 30

A thing is a range of that outcomes whilst you may frivolously divide one quantity through another. In this sense, a thing is likewise called a divisor.

The best not unusualplace thing of or greater numbers is the most important quantity shared through all of the elements.

The best, not unusualplace thing GCF is similar to:

• 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 quantity with the maximum decimal locations
• Count the number of decimal locations in that quantity. Let's name that quantity D.
• For every one of your numbers circulates the decimal D locations to the right. All numbers turn into integers.
• Find the LCM of the set of integers
• For your LCM, circulate the decimal D locations to the left. This is the LCM on your unique set of decimal numbers.

Properties of LCM

The LCM is associative:

LCM(a, b) = LCM(b, a)

The LCM is commutative:

LCM(a, b, c) = LCM(LCM(a, b), c) = LCM(a, LCM(b, c))

The LCM is distributive:

LCM(da, db, dc) = dLCM(a, b, c)

The LCM is associated with the best, not unusualplace thing (GCF):

LCM(a,b) = a × b / GCF(a,b) and