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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 Division

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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
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Step A: Find the Factors Using Division

Factor Methods
Factors of 6
2
6
6/2=3
3
3
⤶
3/3=1
1
⤶
Factors of 12
2
12
12/2=6
2
6
⤶
6/2=3
3
3
⤶
3/3=1
1
⤶
Factors of 18
2
18
18/2=9
3
9
⤶
9/3=3
3
3
⤶
3/3=1
1
⤶

Division Help

1. Start with the smallest prime.
2. Divide the number by this prime.
3. Write the quotient below.
4. Repeat until the quotient is 1.
5. Confirm using multiplication.

What is Division?

The division method for finding factors begins by dividing the given number by the smallest prime factor like 2, 3,.. This process is repeated with successive primes until the quotient is 1.

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 4, 7 and 14.
Solution:
Prime factors of 4 = 2, 2
Prime factors of 7 = 7
Prime factors of 14 = 2, 7
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, 7, 14) = 28. Example 2: Find the LCM of 3, 6 and 9.
Solution:
Prime factors of 3 = 3
Prime factors of 6 = 2, 3
Prime factors of 9 = 3, 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(3, 6, 9) = 18. Example 3: Find the LCM of 6, 7 and 21.
Solution:
Prime factors of 6 = 2, 3
Prime factors of 7 = 7
Prime factors of 21 = 3, 7
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, 7, 21) = 42.

Exercise

1. LCM(12,15,20) = 60. 2. LCM(18,24,36) = 72. 3. LCM(30,40,45) = 360. 4. LCM(10,18,20) = 180. 5. LCM(10,12,15) = 60. 6. LCM(8, 4, 6) = 24. 7. LCM(3,7,14) = 42. 8. LCM(15, 25, 35) = 525. 9. LCM(10,18,20) = 180. 10. LCM(5,9,18) = 90.

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. Enter the three numbers into the calculator.
2. Identify the prime factors of each number using the division method.
3. Draw the venn diagram for given numbers.
4. Take the shared and unshared factors.
5. Multiply together this prime factors.
6. The result is the Least Common Multiple of the three numbers.
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