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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 Venn Diagram Using Factor Tree

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

Step A: Find the Factors Using Factor Tree

Factor Methods
Factors of 6
6
↙
↘
2
3
Factors of 12
12
↙
↘
2
6
↙
↘
2
3
Factors of 18
18
↙
↘
2
9
↙
↘
3
3

Factor Tree Help

1. Always begin with smallest prime.
2. This is the left child of given node.
3. Divide the number by that prime
4. Quotient is the right child of that node.
5. Repeat until right becomes prime factor.
6. Keep tree structure organized.

What is Factor Tree?

The factor tree method is a visual approach used to find the prime factorization of a composite number. It involves breaking down a number into its prime factors by repeatedly dividing it into smaller prime factors until only prime numbers remain which is represent in tree structure.

Step B: Find the LCM Using Venn Diagram

LCM Method
Calculate LCM
2
3
2
3

Venn Diagram Help

1. Draw circles for the numbers.
2. Circle represents the factors.
3. Place common factors in overlaps.
4. Keep unique factors separate.
5. Multiply inside and outside factors.
6. Obtain the LCM.

What is Venn Diagram?

The Venn Diagram Method for LCM uses circles to represent prime factors of numbers. Common factors go in overlaps, unique factors in sections. Multiply within and outside overlaps to get LCM quickly.

Solved Examples

Examples

Example 1: Find the LCM of 20, 30 and 40.
Solution:
Prime factors of 20 = 2, 2, 5
Prime factors of 30 = 2, 3, 5
Prime factors of 40 = 2, 2, 2, 5
Write these prime factors into the venn diagram for each number.
Multiply each prime factor in the venn diagram to find the LCM.
Therefore, LCM(20, 30, 40) = 120. Example 2: Find the LCM of 4, 6 and 12.
Solution:
Prime factors of 4 = 2, 2
Prime factors of 6 = 2, 3
Prime factors of 12 = 2, 2, 3
Write these prime factors into the venn diagram for each number.
Multiply each prime factor in the venn diagram to find the LCM.
Therefore, LCM(4, 6, 12) = 12. Example 3: Find the LCM of 6, 12 and 15.
Solution:
Prime factors of 6 = 2, 3
Prime factors of 12 = 2, 2, 3
Prime factors of 15 = 3, 5
Write these prime factors into the venn diagram for each number.
Multiply each prime factor in the venn diagram to find the LCM.
Therefore, LCM(6, 12, 15) = 60.

Exercise

1. LCM(18,24,36) = 72
 2. LCM(30,45,60) = 180
 3. LCM(8,10,28) = 280
 4. LCM(5,9,18) = 90
 5. LCM(8,12,30) = 120
 6. LCM(2,3,9) = 18
 7. LCM(6,7,21) = 42
 8. LCM(10,12,15) = 60
 9. LCM(15, 25, 35) = 525
 10. LCM(7,21,35) = 105

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. Take the three numbers for which you need to find the LCM.
2. Decompose each number into its prime factors using the tree diagram.
3. Draw the venn diagram for given numbers.
4. Take the shared and unshared factors of numbers.
5. Multiply together this prime factors.
6. The result is the Least Common Multiple of the three numbers.
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