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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 Three Numbers By Exponents Using Ladder

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Exponents Prime Factorization Venn Diagram Division Listing Multiples Ladder
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Answer: LCM of 6, 12, 18 is 36
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Step A: Find the Factors Using Ladder

Factor Methods
Factors of 6
6
/ 2
3
/ 3
1
Factors of 12
12
/ 2
6
/ 2
3
/ 3
1
Factors of 18
18
/ 2
9
/ 3
3
/ 3
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 Exponents

LCM Method
Calculate LCM
6
=
2
1
×
3
1
12
=
2
2
×
3
1
18
=
2
1
×
3
2

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 15, 20 and 30.
Solution:
Prime factorization of 15: 15 = 3, 5
Prime factorization of 20: 20 = 2, 2, 5
Prime factorization of 30: 30 = 2, 3, 5
Take the highest power of each prime factor and multiply them together to get LCM.
Therefore, LCM(15, 20, 30) = 60. Example 2: Find the LCM of 24, 40 and 60.
Solution:
Prime factorization of 24: 24 = 2, 2, 2, 3
Prime factorization of 40: 40 = 2, 2, 2, 5
Prime factorization of 60: 60 = 2, 2, 3, 5
Take the highest power of each prime factor and multiply them together to get LCM.
Therefore, LCM(24, 40, 60) = 120. Example 3: Find the LCM of 3, 5 and 10.
Solution:
Prime factorization of 3: 3 = 3
Prime factorization of 5: 5 = 5
Prime factorization of 10: 10 = 2, 5
Take the highest power of each prime factor and multiply them together to get LCM.
Therefore, LCM(3, 5, 10) = 30.

Exercise

1. LCM(3,9,18) = 18. 2. LCM(18,27,36) = 108. 3. LCM(5,6,15) = 30. 4. LCM(5,8,10) = 40. 5. LCM(6,12,18) = 36. 6. LCM(3,6,18) = 18. 7. LCM(25,30,40) = 600. 8. LCM(8,24,60) = 120. 9. LCM(12,15,10) = 60. 10. LCM(6,15,25) = 150.

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. Input the numbers.
2. Use ladder method for prime factorization.
3. Convert prime factors into their exponent form.
4. Combine unique prime factors with highest exponents.
5. Multiply for the LCM.
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