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 Prime Factorization Using Division

Multiple Numbers Two Numbers Three Numbers

Method

Prime Factorization

Division

Listing Multiples

Ladder

Exponents

Factors

Division

Factor Tree

Ladder

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

Step A: Find the Factors Using Division

Factor Methods

Factors of 18

2	18
		18/2=9
3	9	⤶
		9/3=3
3	3	⤶
		3/3=1
	1	⤶

Factors of 24

2	24
		24/2=12
2	12	⤶
		12/2=6
2	6	⤶
		6/2=3
3	3	⤶
		3/3=1
	1	⤶

Factors of 54

2	54
		54/2=27
3	27	⤶
		27/3=9
3	9	⤶
		9/3=3
3	3	⤶
		3/3=1
	1	⤶

Factors of 60

2	60
		60/2=30
2	30	⤶
		30/2=15
3	15	⤶
		15/3=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 Prime Factorization

LCM Method

Calculate LCM

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

LCM

1080

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 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 2: 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. Example 3: Find the LCM of 8, 12 and 30.
Solution:
Prime factorization of 8: 8 = 2, 2, 2
Prime factorization of 12: 12 = 2, 2, 3
Prime factorization of 30: 30 = 2, 3, 5
Take the common factors once and remaining unique factors.
Multiply them together to get LCM.
Therefore, LCM(8, 12, 30) = 90.

Exercise

1. LCM(12,18,24) = 72
2. LCM(20,30) = 60
3. LCM(15,20,25,30) = 300
4. LCM(12,24,30) = 120
5. LCM(3,9,18) = 18
6. LCM(4,6,12) = 12
7. LCM(6,7,21) = 42
8. LCM(5,9,18) = 90
9. LCM(4,7,14) = 28
10. LCM(4,24,21) = 168

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 factors of each number.
3. Write down the prime factors.
4. Identify the common and uncommon prime factors.
5. Multiply these factors to find the LCM.

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