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LCM
Two Numbers Three Numbers Multiple Numbers Prime Factorization Division Listing Multiples Ladder Exponents Venn Diagram Factor Tree
HCF
Two Numbers Three Numbers Multiple Numbers Prime Factorization Listing Ladder Exponents Venn Diagram Division Factor Tree All Factors By Division All Factors By Multiplication

LCM Of Three Numbers By Division

Three Numbers Two Numbers Multiple Numbers
Method
Division
Prime Factorization
Venn Diagram
Listing Multiples
Ladder
Exponents
Enter Numbers
(Comma Separated)
Steps
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Answer: LCM of 6, 12, 18 is 36

Step B: Find the LCM Using Division

LCM Method
Calculate LCM
2
6
12
18
2
6/
2
12/
2
18/
2
3
6
9
3
↓
6/
2
↓
3
3
9
3
3/
3
3/
3
9/
3
1
1
3
↓
↓
3 /
3
1
1
1
LCM
=
2
x
2
x
3
x
3
=
36

Division Help

1. List all the numbers.
2. Take least common prime.
3. Place them on the left.
4. Divide each number.
5. Write quotients below.
6. Repeat until reaching 1.
7. Multiply factors on left side for LCM.

What is Division?

The division method for finding the Least Common Multiple involves dividing the given numbers by common prime number until the remainder is a prime number or one. LCM will be the product obtained by multiplying all divisors and remaining prime numbers.

Solved Examples

Examples

Example 1: Find the LCM of 6, 12 and 18.
Solution:
Divide the given numbers with least common prime number.
Keep dividing until all numbers are fully divided and remainder is 1.
Here, we multiply the all divisors to calculate the LCM.
Therefore, LCM(6, 12, 18) = 36. Example 2: Find the LCM of 10, 12 and 15.
Solution:
Divide the given numbers with least common prime number.
Keep dividing until all numbers are fully divided and remainder is 1.
Here, we multiply the all divisors to calculate the LCM.
Therefore, LCM(10, 12, 15) = 60. Example 3: Find the LCM of 12, 15 and 16.
Solution:
Divide the given numbers with least common prime number.
Keep dividing until all numbers are fully divided and remainder is 1.
Here, we multiply the all divisors to calculate the LCM.
Therefore, LCM(12, 15, 16) = 240.

Exercise

1. LCM(8,12,18) = 72
 2. LCM(50,60,72) = 1800
 3. LCM(32,40,48) = 480
 4. LCM(21, 24, 36) = 504
 5. LCM(12, 18, 27) = 108
 6. LCM(3,12,16) = 48
 7. LCM(12,30,40) = 120
 8. LCM(20,30,50) = 300
 9. LCM(18,24,60) = 360
 10. LCM(12, 18, 24) = 72

Least Common Multiple (LCM)

What is LCM?

LCM or Least Common Multiple, is the smallest number that is divisible by each of the given numbers without leaving a remainder.
The LCM formula can be expressed as,
LCM Formula:
LCM = (a × b)/ HCF(a,b)
where, a and b = Two terms
HCF(a, b) = Highest common factor of a and b.

How to find LCM?

The Least Common Multiple or LCM can be found using various methods, such as: Prime Factorization MethodDivision MethodListing Multiples MethodLadder MethodExponents MethodVenn Diagram Method

FAQ

What are the steps involved to find LCM?
1. Identify prime factors among the numbers.
2. Divide the numbers by these primes until every number reach 1.
3. Multiply all prime numbers obtained from division for the LCM.
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