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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 Multiple Numbers By Ladder

Multiple Numbers Two Numbers Three Numbers
Method
Ladder
Prime Factorization
Division
Listing Multiples
Exponents
Enter Numbers
(Comma Separated)
Steps
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Answer: LCM of 18, 24, 54, 60 is 1080

Step B: Find the LCM Using Ladder

LCM Method
Calculate LCM
2
2
3
3
18
/ 2
9
⮧
9
/ 3
3
/ 3
1
24
/ 2
12
/ 2
6
/ 3
2
⮧
2
54
/ 2
27
⮧
27
/ 3
9
/ 3
3
60
/ 2
30
/ 2
15
/ 3
5
⮧
5

Ladder Help

1. Identify common factors.
2. Place common factors outside.
3. Divide each number.
4. Write the quotient below.
5. Repeat until no common factors.
6. Multiply all resultant factors with remaining number.
7. Multiplication is the LCM.

What is Ladder?

The ladder method also known as cake method. It is a technique for finding the Least Common Multiple or LCM of numbers by systematically dividing them with their smallest common prime factors until no common factor found, noting the divisors leftward as well as downward. Finally, the LCM is obtained by multiplying these divisors.

Solved Examples

Examples

Example 1: Find the LCM of 4 and 6.
Solution:
Start with the two numbers, 4 and 6.
LCM is the product of common and non common factors.
Therefore, LCM(4, 6) = 12. Example 2: Find the LCM of 10 and 15.
Solution:
Start with the two numbers, 10 and 15.
LCM is the product of common and non common factors.
Therefore, LCM(10, 15) = 30. Example 3: Find the LCM of 8 and 12.
Solution:
Start with the two numbers, 8 and 12.
LCM is the product of common and non common factors.
Therefore, LCM(8, 12) = 24.

Exercise

1. LCM(9,12,15,18) = 180
 2. LCM(15,27) = 135
 3. LCM(20,35) = 140
 4. LCM(7,14,21) = 42
 5. LCM(16,24) = 48
 6. LCM(9,12,18) = 36
 7. LCM(18, 24, 32) = 288
 8. LCM(6,9,15,18) = 90
 9. LCM(10,15,15,20) = 60
 10. LCM(8,10,12,16) = 240

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. Write down the given numbers.
2. Create a ladder diagram to find the prime factorization of each number.
3. Multiplying the factors on the left side that is common factors and the factors at the bottom that is uncommon factors.
4. Multiply these common and remaining unique numbers to get the LCM.
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