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 unearths the LCM and indicates the paintings the usage of five special methods:
Find all of the top elements of every given variety.
List all of the top numbers determined, as in many instances as they arise most customarily for anyone 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 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 top numbers determined as regularly as everyone takes place most customarily 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 determined as regularly as everyone takes place most customarily 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 determined, the usage of the best exponent determined 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 determined, as in many instances as they arise most customarily for anyone 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 determined, as in many instances as they arise most customarily for anyone 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 of 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 field technique, the thing field technique, and the grid technique of shortcuts to locate the LCM. The bins and grids may appearance a bit special, 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)
Cake / Ladder
10
12
15
75
Divide the layer numbers with the aid of using a top variety this is calmly divisible into or greater numbers with inside the layer and produce down the end result into the subsequent layer.
Cake / Ladder
2
10
12
15
75
five
6
If any variety inside the layer isn't calmly divisible simply deliver down that variety.
Cake / Ladder
Continue dividing cake layers with the aid of using top numbers.
When there aren't any greater primes that calmly divided into or greater numbers you're done.
Cake / Ladder
The LCM is made of numbers inside 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
Division Table
10
18
25
Starting with the bottom top numbers, divide the row of numbers with the aid of using a top variety this is calmly divisible into as a minimum certainly considered one among your numbers and produce down the end result into the subsequent desk row.
If any variety inside the row isn't calmly divisible simply deliver down that variety.
Division Table
2101825
five925
Continue dividing rows with the aid of using top numbers that divide calmly into a minimum of one variety.
When the ultimate row of effects is all 1's you're done.
The LCM is made of the top numbers inside the first column.
LCM = 2 × 3 × 3 × five × five
LCM = 450
Therefore, LCM(10, 18, 25) = 450
How to Find LCM with the aid of using GCF
The formulation to locate the LCM the usage 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 with the aid of using GCF formulation to calculate (6×10)/2 = 60/2 = 30
So LCM(6,10) = 30
A thing is a variety of that effects whilst you may calmly divide one variety with the aid of using another. In this sense, a thing is likewise called a divisor.
The finest not unusual place thing of or greater numbers is the biggest variety shared with the aid of using all of the elements.
The finest not unusual place 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 variety with the maximum decimal locations
Count the variety of decimal locations in that variety. Let's name that variety D.
For every one of your numbers circulates the decimal D locations to the right. All numbers become integers.
Find the LCM of the set of integers
For your LCM, circulate the decimal D locations to the left. This is the LCM in your authentic 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 finest not unusual place thing (GCF):
LCM(a,b) = a × b / GCF(a,b) and GCF(a,b) = a × b / LCM(a,b)
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