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 Multiple Numbers By Exponents Using Factor Tree

Multiple Numbers Two Numbers Three Numbers

Method

Exponents Prime Factorization Division Listing Multiples Ladder

Factors

Factor Tree Division Ladder

Enter Numbers (Comma Separated)
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Answer: LCM of 18, 24, 54, 60 is 1080

Step A: Find the Factors Using Factor Tree

Factor Methods

Factors of 18

		18
	↙		↘
2				9
			↙		↘
		3				3

Factors of 24

		24
	↙		↘
2				12
			↙		↘
		2				6
					↙		↘
				2				3

Factors of 54

		54
	↙		↘
2				27
			↙		↘
		3				9
					↙		↘
				3				3

Factors of 60

		60
	↙		↘
2				30
			↙		↘
		2				15
					↙		↘
				3				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 Exponents

LCM Method

Calculate LCM

18 =	2 ¹ × 3 ²
24 =	2 ³ × 3 ¹
54 =	2 ¹ × 3 ³
60 =	2 ² × 3 ¹ × 5 ¹

LCM

1080

Exponents Help

1. List the Prime Factors with power.
2. Identify Unique Prime Factors.
3. Select factors with high power.
4. Multiply to Find LCM.

What is Exponents?

Exponents method simplifies finding the lowest common multiple or LCM by listing all the prime factors of each number and then selecting the highest power of each common prime factor to obtain the LCM.

Solved Examples

Examples

Example 1: Find the LCM of 4 and 6.
Solution:
Prime factorization of 4: 4 = 2, 2
Prime factorization of 6: 6 = 2, 3
Take the highest power of each prime factor and multiply them together to get LCM.
Therefore, LCM(4, 6) = 12. Example 2: Find the LCM of 10 and 15.
Solution:
Prime factorization of 10: 10 = 2, 5
Prime factorization of 15: 15 = 3, 5
Take the highest power of each prime factor and multiply them together to get LCM.
Therefore, LCM(10, 15) = 30. Example 3: Find the LCM of 8 and 12.
Solution:
Prime factorization of 8: 8 = 2, 2, 2
Prime factorization of 12: 12 = 2, 2, 3
Take the highest power of each prime factor and multiply them together to get LCM.
Therefore, LCM(8, 12) = 24.

Exercise

1. LCM(14,21,35) = 210. 2. LCM(10,12,15,20) = 60. 3. LCM(14,21,28,35) = 420. 4. LCM(9,18) = 18. 5. LCM(16,24,32) = 96. 6. LCM(5,10,15) = 30. 7. LCM(7,14,21) = 42. 8. LCM(11,22,33) = 66. 9. LCM(12,18,24) = 72. 10. LCM(9,15,27) = 135.

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 factor trees to find the prime factorization of each number.
3. Identify unique prime factors with highest powers.
4. Multiply these factors to find the LCM.

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