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 Division

Two Numbers Three Numbers Multiple Numbers

Method

Venn Diagram Prime Factorization Division Listing Multiples Ladder Exponents

Factors

Division Factor Tree Ladder

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

Step A: Find the Factors Using Division

Factor Methods

Factors of 30

2	30
		30/2=15
3	15	⤶
		15/3=5
5	5	⤶
		5/5=1
	1	⤶

Factors of 75

3	75
		75/3=25
5	25	⤶
		25/5=5
5	5	⤶
		5/5=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

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 12 and 8.
Solution:
Prime factors of 12 = 2, 2, 3
Prime factors of 8 = 2, 2, 2
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(12, 8) = 24. Example 2: Find the LCM of 18 and 24.
Solution:
Prime factors of 18 = 2, 3, 3
Prime factors of 24 = 2, 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(18, 24) = 72. Example 3: Find the LCM of 10 and 25.
Solution:
Prime factors of 10 = 2, 5
Prime factors of 25 = 5, 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(10, 25) = 50.

Exercise

1. LCM(12,18) = 36. 2. LCM(11,22) = 22. 3. LCM(18,24) = 72. 4. LCM(30,40) = 120. 5. LCM(6, 15) = 30. 6. LCM(24, 36) = 72. 7. LCM(9, 12) = 36. 8. LCM(16, 40) = 80. 9. LCM(4, 5) = 20. 10. LCM(8, 10) = 40.

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 division to find the prime factorization of each number.
3. Draw a Venn diagram with circles representing the prime factors of each number.
4. Multiply together this prime factors.
5. The result is the Least Common Multiple of the numbers.

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