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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 Prime Factorization Using Division

Two Numbers Three Numbers Multiple Numbers
Method
Prime Factorization
Division
Listing Multiples
Ladder
Exponents
Venn Diagram
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Answer: LCM of 30, 75 is 150

Step A: Find the Factors Using Division

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

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 18 and 24.
Solution:
Prime factorization of 18: 18 = 2, 3, 3
Prime factorization of 24: 24 = 2, 2, 2, 3
Take the common factors once and remaining unique factors.
Multiply them together to get LCM.
Therefore, LCM(18, 24) = 72. Example 2: Find the LCM of 30 and 45.
Solution:
Prime factorization of 30: 30 = 2, 3, 5
Prime factorization of 45: 45 = 3, 3, 5
Take the common factors once and remaining unique factors.
Multiply them together to get LCM.
Therefore, LCM(30, 45) = 90. Example 3: Find the LCM of 2 and 10.
Solution:
Prime factorization of 2: 2 = 2
Prime factorization of 10: 10 = 2, 5
Take the common factors once and remaining unique factors.
Multiply them together to get LCM.
Therefore, LCM(2, 10) = 10.

Exercise

1. LCM(8,12) = 24
 2. LCM(36,48) = 144
 3. LCM(27,36) = 108
 4. LCM(24,36) = 72
 5. LCM(3,7) = 21
 6. LCM(13, 17) = 221
 7. LCM(6,15) = 30
 8. LCM(11,15) = 165
 9. LCM(60,90) = 180
 10. LCM(35,48) = 1680

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 two numbers you want to find LCM.
2. Identify the prime factors of each number using the division method.
3. List all prime factors for each number.
4. Combine common prime factors at once and remaining uncommon factors.
5. Multiply these common with uncommon factors to calculate the LCM.
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