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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 Division

Three Numbers Two Numbers Multiple Numbers
Method
Exponents
Prime Factorization
Venn Diagram
Division
Listing Multiples
Ladder
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(Comma Separated)
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Answer: LCM of 6, 12, 18 is 36

Step A: Find the Factors Using Division

Factor Methods
Factors of 6
2
6
6/2=3
3
3
⤶
3/3=1
1
⤶
Factors of 12
2
12
12/2=6
2
6
⤶
6/2=3
3
3
⤶
3/3=1
1
⤶
Factors of 18
2
18
18/2=9
3
9
⤶
9/3=3
3
3
⤶
3/3=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 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 10, 20 and 30.
Solution:
Prime factorization of 10: 10 = 2, 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(10, 20, 30) = 60. Example 2: Find the LCM of 16, 24 and 40.
Solution:
Prime factorization of 16: 16 = 2, 2, 2, 2
Prime factorization of 24: 24 = 2, 2, 2, 3
Prime factorization of 40: 40 = 2, 2, 2, 5
Take the highest power of each prime factor and multiply them together to get LCM.
Therefore, LCM(16, 24, 40) = 240. Example 3: Find the LCM of 40, 50 and 20.
Solution:
Prime factorization of 40: 40 = 2, 2, 2, 5
Prime factorization of 50: 50 = 2, 5, 5
Prime factorization of 20: 20 = 2, 2, 5
Take the highest power of each prime factor and multiply them together to get LCM.
Therefore, LCM(40, 50, 20) = 200.

Exercise

1. LCM(12,18,24) = 72
 2. LCM(15,25,30) = 150
 3. LCM(21,28,35) = 420
 4. LCM(27,36,54) = 108
 5. LCM(14,21,35) = 210
 6. LCM(25,30,45) = 450
 7. LCM(16,20,24) = 240
 8. LCM(42,56,70) = 840
 9. LCM(16,40,64) = 320
 10. LCM(27,36,45) = 540

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 your numbers into the calculator.
2. Use division method for prime factorization.
3. Convert prime factors into their exponent form.
4. Multiply the unique prime factors with highest exponent.
5. Obtain the LCM.
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