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 Two Numbers By Venn Diagram Using Factor Tree

Two Numbers Three Numbers Multiple Numbers

Method

Venn Diagram Prime Factorization Division Listing Multiples Ladder Exponents

Factors

Factor Tree Division Ladder

Enter Numbers (Comma Separated)
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Answer: LCM of 30, 75 is 150

Step A: Find the Factors Using Factor Tree

Factor Methods

Factors of 30

		30
	↙		↘
2				15
			↙		↘
		3				5

Factors of 75

		75
	↙		↘
3				25
			↙		↘
		5				5

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

LCM

150

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 9 and 12.
Solution:
Prime factors of 9 = 3, 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(9, 12) = 36. Example 2: Find the LCM of 24 and 36.
Solution:
Prime factors of 24 = 2, 2, 2, 3
Prime factors of 36 = 2, 2, 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(24, 36) = 72. Example 3: Find the LCM of 40 and 56.
Solution:
Prime factors of 40 = 2, 2, 2, 5
Prime factors of 56 = 2, 2, 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(40, 56) = 280.

Exercise

1. LCM(4,6) = 12. 2. LCM(10,25) = 50. 3. LCM(20,35) = 140. 4. LCM(12, 36) = 36. 5. LCM(45,75) = 225. 6. LCM(35, 15) = 105. 7. LCM(16, 20) = 80. 8. LCM(15, 45) = 45. 9. LCM(48, 60) = 240. 10. LCM(30, 45) = 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 Method Division Method Listing Multiples Method Ladder Method Exponents Method Venn Diagram Method

FAQ

What are the steps involved to find LCM?

1. Write down the given numbers.
2. Use the factor tree method to find the prime factors of both number.
3. Draw a Venn diagram with circles representing the prime factors of both number.
4. Multiply together this prime factors.
5. The result is the Least Common Multiple of the numbers.

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