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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 Ladder

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Answer: LCM of 30, 75 is 150
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Step A: Find the Factors Using Ladder

Factor Methods
Factors of 30
30
/ 2
15
/ 3
5
/ 5
1
Factors of 75
75
/ 3
25
/ 5
5
/ 5
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
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 15 and 25.
Solution:
Prime factorization of 15: 15 = 3, 5
Prime factorization of 25: 25 = 5, 5
Take the common factors once and remaining unique factors.
Multiply them together to get LCM.
Therefore, LCM(15, 25) = 75. Example 3: Find the LCM of 10 and 15.
Solution:
Prime factorization of 10: 10 = 2, 5
Prime factorization of 15: 15 = 3, 5
Take the common factors once and remaining unique factors.
Multiply them together to get LCM.
Therefore, LCM(10, 15) = 30.

Exercise

1. LCM(24,36) = 72. 2. LCM(16,28) = 112. 3. LCM(19,30) = 570. 4. LCM(8,10) = 40. 5. LCM(36,85) = 3060. 6. LCM(12,8) = 24. 7. LCM(60,84) = 420. 8. LCM(108,120) = 1080. 9. LCM(12,18) = 36. 10. LCM(12,80) = 240.

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 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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