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 Ladder

Two Numbers Three Numbers Multiple Numbers

Method

Ladder Prime Factorization Division Listing Multiples Exponents Venn Diagram

Enter Numbers (Comma Separated)
		Steps
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Answer: LCM of 30, 75 is 150

Step B: Find the LCM Using Ladder

LCM Method

Calculate LCM

30 / 3
	10 / 5

75 / 3
	25 / 5

LCM

150

Ladder Help

1. Identify common factors.
2. Place common factors outside.
3. Divide each number.
4. Write the quotient below.
5. Repeat until no common factors.
6. Multiply all resultant factors with remaining number.
7. Multiplication is the LCM.

What is Ladder?

The ladder method also known as cake method. It is a technique for finding the Least Common Multiple or LCM of numbers by systematically dividing them with their smallest common prime factors until no common factor found, noting the divisors leftward as well as downward. Finally, the LCM is obtained by multiplying these divisors.

Solved Examples

Examples

Example 1: Find the LCM of 24 and 15.
Solution:
Start with the two numbers, 24 and 15.
LCM is the product of common and non common factors.
Therefore, LCM(24, 15) = 120. Example 2: Find the LCM of 30 and 50.
Solution:
Start with the two numbers, 30 and 50.
LCM is the product of common and non common factors.
Therefore, LCM(30, 50) = 150. Example 3: Find the LCM of 18 and 24.
Solution:
Start with the two numbers, 18 and 24.
LCM is the product of common and non common factors.
Therefore, LCM(18, 24) = 72.

Exercise

1. LCM(14,21) = 42. 2. LCM(28,35) = 140. 3. LCM(36,48) = 144. 4. LCM(36,72) = 72. 5. LCM(16,40) = 80. 6. LCM(48,72) = 144. 7. LCM(96,40) = 480. 8. LCM(24,32) = 96. 9. LCM(90,30) = 90. 10. LCM(12,90) = 180.

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. Input two numbers into the calculator.
2. Apply Ladder Division, organizing prime factors in a ladder structure.
3. Ascend the ladder, multiplying the factors on the left side that is common factors and the factors at the bottom that is uncommon factors.
4. Multiply these common and remaining unique numbers to get the LCM.

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