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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 Multiple Numbers By Exponents Using Ladder

Multiple Numbers Two Numbers Three Numbers
Method
Exponents Prime Factorization Division Listing Multiples Ladder
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Answer: LCM of 18, 24, 54, 60 is 1080

Step A: Find the Factors Using Ladder

Factor Methods
Factors of 18
18
/ 2
9
/ 3
3
/ 3
1
Factors of 24
24
/ 2
12
/ 2
6
/ 2
3
/ 3
1
Factors of 54
54
/ 2
27
/ 3
9
/ 3
3
/ 3
1
Factors of 60
60
/ 2
30
/ 2
15
/ 3
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 Exponents

LCM Method
Calculate LCM
18
=
2
1
×
3
2
24
=
2
3
×
3
1
54
=
2
1
×
3
3
60
=
2
2
×
3
1
×
5
1

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 4 and 16.
Solution:
Prime factorization of 4: 4 = 2, 2
Prime factorization of 16: 16 = 2, 2, 2, 2
Take the highest power of each prime factor and multiply them together to get LCM.
Therefore, LCM(4, 16) = 16. Example 2: Find the LCM of 10 and 15.
Solution:
Prime factorization of 10: 10 = 2, 5
Prime factorization of 15: 15 = 3, 5
Take the highest power of each prime factor and multiply them together to get LCM.
Therefore, LCM(10, 15) = 30. Example 3: Find the LCM of 8 and 12.
Solution:
Prime factorization of 8: 8 = 2, 2, 2
Prime factorization of 12: 12 = 2, 2, 3
Take the highest power of each prime factor and multiply them together to get LCM.
Therefore, LCM(8, 12) = 24.

Exercise

1. LCM(20,30,40) = 120
 2. LCM(14,21) = 42
 3. LCM(24,32) = 96
 4. LCM(9,15,18,21) = 630
 5. LCM(16,24,32) = 96
 6. LCM(5,10,15) = 30
 7. LCM(12,18,24) = 72
 8. LCM(15,25,35) = 525
 9. LCM(16,32,48) = 96
 10. LCM(21,28,35,42 ) = 420

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 given numbers.
2. Use the ladder technique to find the prime factors of each number.
3. Identify unique prime factors with highest powers.
4. Multiply these factors to find the LCM.
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