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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 Two Numbers By Venn Diagram Using Ladder

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Venn Diagram Prime Factorization Division Listing Multiples Ladder Exponents
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Answer: LCM of 30, 75 is 150
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Step A: Find the Factors Using Ladder

Factor Methods
Factors of 30
30
/ 2
15
/ 3
5
/ 5
1
Factors of 75
75
/ 3
25
/ 5
5
/ 5
1

Ladder Help

1. Start with smallest prime factor.
2. Divide the number by it.
3. Write prime factor on right.
4. Place the quotient below.
5. Repeat with same prime factor.
6. Move to next prime factor if not divisible.
7. Continue until 1.
8. Numbers on the right are prime factors.

What is Ladder?

The ladder method involves repeatedly dividing the number by the smallest prime numbers, starting from 2 until the quotient becomes 1. The divisors are arranged in a ladder formation, hence the method name is ladder.

Step B: Find the LCM Using Venn Diagram

LCM Method
Calculate LCM
2
5
3
5

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 35 and 15.
Solution:
Prime factors of 35 = 5, 7
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(35, 15) = 105. Example 2: Find the LCM of 8 and 10.
Solution:
Prime factors of 8 = 2, 2, 2
Prime factors of 10 = 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(8, 10) = 40. Example 3: Find the LCM of 60 and 120.
Solution:
Prime factors of 60 = 2, 2, 3, 5
Prime factors of 120 = 2, 2, 2, 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(60, 120) = 120.

Exercise

1. LCM(15,25) = 75. 2. LCM(33,44) = 132. 3. LCM(27,36) = 108. 4. LCM(10,15) = 30. 5. LCM(9, 12) = 36. 6. LCM(30,40) = 120. 7. LCM(20, 80) = 80. 8. LCM(24, 36) = 72. 9. LCM(11, 15) = 165. 10. LCM(36, 45) = 180.

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. Use the ladder method 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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