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 Factor Tree

Three Numbers Two Numbers Multiple Numbers

Method

Prime Factorization Venn Diagram Division Listing Multiples Ladder Exponents

Factors

Factor Tree Division Ladder

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

Step A: Find the Factors Using Factor Tree

Factor Methods

Factors of 6

		6
	↙		↘
2				3

Factors of 12

		12
	↙		↘
2				6
			↙		↘
		2				3

Factors of 18

		18
	↙		↘
2				9
			↙		↘
		3				3

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 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 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 2: Find the LCM of 8, 4 and 6.
Solution:
Prime factorization of 8: 8 = 2, 2, 2
Prime factorization of 4: 4 = 2, 2
Prime factorization of 6: 6 = 2, 3
Take the common factors once and remaining unique factors.
Multiply them together to get LCM.
Therefore, LCM(8, 4, 6) = 24. 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(12,15,18) = 180. 2. LCM(20,30,40) = 120. 3. LCM(36,48,72) = 144. 4. LCM(10,12,15) = 60. 5. LCM(6,7,21) = 42. 6. LCM(12,24,30) = 120. 7. LCM(2,3,9) = 18. 8. LCM(4,6,12) = 12. 9. LCM(9,16,34) = 2448. 10. LCM(7,21,35) = 105.

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. Take the three numbers for which you need to find the LCM.
2. Decompose each number into its prime factors using the factor tree method.
3. Create factor trees for each number to visualize the prime factors.
4. Identify the common prime factors shared by both numbers.
5. Multiply together the common prime factors with any remaining prime factors unique to each number.
6. The result is the Least Common Multiple or LCM of the three numbers.

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