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 Prime Factorization Using Ladder

Three Numbers Two Numbers Multiple Numbers

Method

Prime Factorization Venn Diagram Division Listing Multiples Ladder Exponents

Factors

Ladder Factor Tree Division

Enter Numbers (Comma Separated)
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Answer: LCM of 6, 12, 18 is 36

Step A: Find the Factors Using Ladder

Factor Methods

Factors of 6

6 / 2
	3 / 3
		1

Factors of 12

12 / 2
	6 / 2
		3 / 3
			1

Factors of 18

18 / 2
	9 / 3
		3 / 3
			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 Prime Factorization

LCM Method

Calculate LCM

6 =	2 × 3
12 =	2 × 2 × 3
18 =	2 × 3 × 3

LCM

Prime Factorization Help

1. Express numbers as primes.
2. Select common primes.
3. Include each prime once.
4. Also take remaining prime
5. Multiply all selected primes.
6. Multiplication is the LCM.

What is Prime Factorization?

The prime factorization method is an effective approach to find the Least Common Multiple or LCM of two or more numbers. It is the process of expressing a composite number as the product of its prime factors, where each prime factor is a prime number and cannot be further decomposed.

Solved Examples

Examples

Example 1: Find the LCM of 6, 7 and 21.
Solution:
Prime factorization of 6: 6 = 2, 3
Prime factorization of 7: 7 = 7
Prime factorization of 21: 21 = 3, 7
Take the common factors once and remaining unique factors.
Multiply them together to get LCM.
Therefore, LCM(6, 7, 21) = 42. Example 2: Find the LCM of 15, 25 and 35.
Solution:
Prime factorization of 15: 15 = 3, 5
Prime factorization of 25: 25 = 5, 5
Prime factorization of 35: 35 = 5, 7
Take the common factors once and remaining unique factors.
Multiply them together to get LCM.
Therefore, LCM(15, 25, 35) = 525. Example 3: Find the LCM of 6, 12 and 18.
Solution:
Prime factorization of 6: 6 = 2, 3
Prime factorization of 12: 12 = 2, 2, 3
Prime factorization of 18: 18 = 2, 3, 3
Take the common factors once and remaining unique factors.
Multiply them together to get LCM.
Therefore, LCM(6, 12, 18) = 36.

Exercise

1. LCM(12,18,24) = 72. 2. LCM(16,24,32) = 96. 3. LCM(15,20,30) = 60. 4. LCM(10,12,15) = 60. 5. LCM(3,9,18) = 18. 6. LCM(45,60,75) = 900. 7. LCM(18,24,60) = 360. 8. LCM(10,18,20) = 180. 9. LCM(10,15,75) = 150. 10. LCM(20,30,40) = 120.

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. Enter the three numbers into the calculator.
2. Identify the prime factors of each number using the ladder method.
3. List all prime factors for each number.
4. Combine common prime factors at once with remaining uncommon factors.
5. Multiply these common and uncommon factors to calculate the LCM.

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